MATHEMATICS MCQ | Class 10 | Chapter 8
TRIGONOMETRY

Q 1) Trigonometric ratios are only applicable to which kind of triangles?

a) Right-angled triangles b) Any type of triangles
c) Acute angled triangles d) Obtuse angled triangles

Ans a
Q 2) The value of $\frac{sin\theta }{cos\theta }$ equals to
a) tan θ b) cot θ c) cosec θ d) sec θ

Ans: a

Q 3) Trigonometric ratios are
a) sine, cosine and cotangent
b) sine, tangent, cotangent and secant
c) sine, cosine, tangent, cotangent, secant and cosecant
d) tangent, cotangent and secant

Ans: c

Q 4) Choose the correct reciprocal ratios.
a) Tan θ, Sec θ b) Cosec θ, Sec θ
c) Sec θ, Sin θ d) Tan θ, Cot θ

Ans: d

Q 5) What is the value of sec θ when θ is 45°?
a) √3 b) 1 c) 0 d) √2

Ans: d

Q 6) What is the value of sin 0° + cos 0° ?
a) 0 b) 2 c) 1 d) ∞

Ans: c

Q 7) Evaluate cos 30° sin 60° + cos 60° sin 30°.
a) 2 b) 0 c) 1 d) ∞

Ans: c

Q 8) The value of Cosec 0° is
a) Not defined b) 1 c) 0 d) 2

Ans: a

Q 9) The value of sin 90° + cos 0° + √2 cos 45° is
a) 2 b) 1 c) 4 d) 3

Ans: d

Q 10) The value of Cosec 90° is
a) 0 b) 2 c) 1 d) √3

Ans: c

Q 11) If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.
(a) 45° (b) 30° (c) 29° (d) 52°

Ans: c

Q 12) Evaluate sin² 30.
a) 2 b) 0 c) 1/ 4 d) ∞

Ans: c

Q 13) In ∆ ABC, right - angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:
(a) 12/ 7 (b) 24/ 7 (c) 20/ 7 (d) 7/ 24
Ans: b

Q 14) The value of sin² 90° + √2 cos 45° + √3 cot 30° is

a) 2 b) 0 c) 4 d) 5

Ans: d

Q 15) The product of sec 30° and cos 60° is
a) 0 b) 2 c) 1 $d)\: \: \: \frac{1}{\sqrt{3}}$

Ans: d

Q 16) Which among these are complementary angles?
a) ∠A + ∠B = 90° b) ∠A + ∠B = 180°
c) ∠A + ∠B = 60° d) ∠A + ∠B = 45°

Ans: a

Q 17) Evaluate tan 75° + cot 65°.
a) Cot 25° + Tan 15° b) Cot 25° – Tan 15°
c) Cot 15° + Tan 25° d) Cot 15° – Tan 25°

Ans: c

Q 18) Evaluate sec 65° + cosec 75°.
a) Cosec 25° + Sec 15° b) Cosec 25° – Sec 15°
c) Cosec 15° + Sec 25° d) Cosec 15° – Sec 25°

Ans: a

Q 19) If in ΔABC, ∠C = 90°, then sin (A + B) =
(a) 0 (b) 1/2 (c) 2 (d) 1

Ans: d

Q 20) Find the correct trigonometric identity.
a) tan²θ = sec²θ – 1 b) tan²θ + sec²θ = 1
c) tan²θ – sec²θ = 1 d) tan²θ = sec²θ + 1

Ans: a

Q 21) Evaluate (cosec θ – cot θ) (cosec θ + cot θ).
a) 0 b) 1 c) 2 d) 3

Ans: b

Q 22) Evaluate cosec θ sec θ.
a) cos θ + tan θ b) cos θ – tan θ
c) tan θ – cot θ d) cot θ + tan θ

Ans: d

Q 23) (Sin 30° + cos 60°) - (sin 60° + cos 30°) is equal to:
(a) 0
(b) 1 + 2√3
(c) 1-√3
(d) 1+√3

Ans: c

Q 24) If 3 cot θ = 2, then the value of tan θ
$a)\: \: \: \frac{2}{3}$
$b)\: \: \: \frac{3}{2}$
$c)\: \: \: \frac{3}{\sqrt{13}}$
$d)\: \: \: \frac{2}{\sqrt{13}}$

Ans: b

Q 25) Evaluate sec² A + (1 + tan A) (1 – tan A).

a) 3
b) 0
c) 2
d) 1

Ans: c

Q 26) (1 + cosec θ) (1 – cosec θ) + cot²θ is
a) Cot ⁡θ
b) 0
c) 1
d) Tan θ

Ans: b
Q 27) The value of $\frac{tan60^{o}}{cot30^{o}}$ is equal to:
(a) 0
(b) 1
(c) 2
(d) 3

Ans: b

Q 28) The value of (Cos θ + sin θ)² + (Cos θ - sin θ)²is
a) -2
b) 0
c) 1
d) 2

Ans: d

Q 29) 1 – cos²A is equal to:
(a) sin²A

(b) tan²A

(c) 1 – sin²A

(d) sec²A

Ans: a

Q 30) Value of sin (90° – A) =
(a) sin A
(b) tan A
(c) cos A
(d) cosec A

Ans: c

Q 31) sin (90° – A) and cos A are:
(a) Different
(b) Same
(c) Not related
(d) None of the above

Ans: b
Q 32) Find the value of $\frac{2tan30^{o}}{1-tan^{2}30^{o}}$
(a) sin60°
(b) cos60°
(c) tan60°
(d) sin30°

Ans: c

Q 33) The value of sin 60° cos 30° + sin 30° cos 60° is:
(a) 0
(b) 1
(c) 2
(d) 4

Ans: b
Q 34) Evaluate $\frac{tan65^{o}}{cot25^{o}}$
(a) 0
(b) 1
(c) 1 / 2
(d) 2

Ans: b

Q 35) sin 2A = 2 sin A is true when A =
(a) 30°
(b) 45°
(c) 0°
(d) 60°

Ans: c

Q 36) The value of (sin 45° + cos 45°) is
(a) 1/√2
(b) 1
(c) √3/2
(d) √2

Ans: d

Q 37) If sin A = 1/2 , then the value of cot A is
(a) √3
(b) 1/√3
(c) √3/2
(d) 1

Ans: a

Q 38) If A, B and C are interior angles of a ΔABC then Cos(B+C)/2 is equal to

$a)\: \: \: sin\left ( \frac{A}{2} \right )$

$b)\: \: \: -sin\left ( \frac{A}{2} \right )$

$c)\: \: \: cos\left ( \frac{A}{2} \right )$

$d)\: \: \: -cos\left ( \frac{A}{2} \right )$

Ans: a

Q 39) If ∆ABC is right angled at C, then the value of cos(A + B) is
(a) 1/2
(b) 1
(c) 0
(d) √3/2

Ans: c

Q 40) If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to
(a) √3
(b) √3/2
(c) 1/2
(d) 1

Ans: d

Q 41) $\frac{1-cosA}{sinA}\: \: is\: equal\: to\: :$

$a)\: \: \: \frac{sinA}{1-cosA}$

$b)\: \: \: \frac{sinA}{1+cosA}$

$c)\: \: \: \frac{cosA}{1-cosA}$

$d)\: \: \: \frac{cosA}{1+cosA}$

Ans: b

Q 42) The value of (tan 1° tan 2° tan 3° … tan 89°) is
(a) 0
(b) 1
(c) 2
(d) ½
Ans: b

Explanation:
tan 1° tan 2° tan 3°…tan 89°
= [tan 1° tan 2°…tan 44°] tan 45° [tan (90° – 44°) tan (90° – 43°)…tan (90° – 1°)]
= [tan 1° tan 2°…tan 44°] [cot 44° cot 43°…cot 1°] × [tan 45°]
= [(tan 1°× cot 1°) (tan 2°× cot 2°)…(tan 44°× cot 44°)] × [tan 45°]
= 1 × 1 × 1 × 1 × …× 1 {since tan A × cot A = 1 and tan 45° = 1} = 1

Q 43) The value of sin² 30° – cos² 30° is

$a)\: \: \frac{-1}{2}$

$b)\: \: \frac{\sqrt{3}}{2}$

$c)\: \: \frac{3}{2}$

$d)\: \: \frac{2}{3}$

Ans: a

Q 44) If sin A = 8/ 17 what will be the value of cos A sec A ?

a) 2

b) -1

c) 1

d) 0

Ans: c

Q 45) If tan α = √3 and cosec β = 1, then the value of α – β ?

a) -30°

b) 30°

c) 90°

d) 60°

Ans: a

Q 46) In triangle ABC, right angled at C, then the value of cosec (A + B) is

a) 2

b) 0

c) 1

d) ∞

Ans: c

Q 47) What is the value of cos A sec A + sin A cosec A – tan A cot A?

a) 0

b) 2

c) 1

d) 3

Ans: c

Q 48) Which of the following is true ?

a) sin 2A = 2sinA

b) tan A = $\frac{sin}{cos}A$

c) sin(A + B) = sin A + sin B

d) (sin A)² = sin² A

Ans: d

Q 49) If 15 cot A = 8 then cos A =

$a)\: \: \frac{15}{17}$

$b)\: \: \frac{8}{15}$

$c)\: \: \frac{8}{17}$

$d)\: \: \frac{15}{8}$

Ans: c

Q 50) If $\frac{1+cos\theta }{1-cos\theta }=\frac{16}{9}$ , then find $\frac{1+tan\theta }{1-tan\theta }$

$a)\: \: \: \frac{17}{31}$

$b)\: \: \: \frac{15}{29}$

$c)\: \: \: \frac{29}{-15}$

$d)\: \: \: \frac{-31}{17}$

Ans: d

Q 51) If $\sqrt{3}$ tanθ = 3 sin θ, then the value of secθ is

a) $\sqrt{3}$

b) $\sqrt{2}$

c) $\frac{1}{\sqrt{2}}$

d) $\frac{1}{\sqrt{3}}$

Ans: a

Q 52) If 3 cot θ = 4, then the value of $\frac{3sin\theta +4cos\theta }{3sin\theta -4cos\theta }$ is

$a)\: \: \frac{25}{7}$

$b)\: \: \frac{-25}{7}$

$c)\: \: \frac{7}{25}$

$d)\: \: 0$

Ans: b

Q 53) Evaluate: $\frac{tan60^{o}-tan30^{o}}{1+tan60^{o}tan30^{o}}$

a) tan 60^o

b) cos 30^o

c) tan 30^o

d) sin 30^o

Ans: c

Q 54) If tan (2A + B) = $\sqrt{3}$ and cot (3A – B ) = $\sqrt{3}$

a) 24^o, 18^o

b) 18^o, 24^o

c) 24^o, 28^o

d) 20^o, 24^o

Ans: b

Q 55) If cos (2A - B) = sin (A + 2B ) = $\frac{\sqrt{3}}{2}$

a) 24^o, 18^o

b) 18^o, 26^o

c) 28^o, 24^o

d) 24^o, 30^o

Ans: a

Q 56) Sin a = $\frac{1}{2}$ , cos b = $\frac{1}{2}$ , then (a + b) =

a) 0^o

b) 30^o

c) 60^o

d) 90^o

Ans: d

Q 57) If θ is an acute angle and tanθ + cot θ = 2, find tan¹⁰ θ + cot ¹⁰ θ

a) 2¹⁰

b) 2

c) 2⁵

d) 1

Ans: b

Solution Hint

tanθ + 1/ tanθ = 2 ⇒ tan² θ - 2tan θ + 1 = 0

Factorise this equation and then solving it we get θ = 45^o

Using this value of θ and find the required value

Q 58) If θ is an acute angle and sinθ + cosecθ = 2, find sin¹⁵ θ + cosec ¹⁵ θ

a) 2¹⁵

b) 1

c) 2

d) 0

Ans: c

Solution Hint

sinθ + cosecθ = 2 = 1 + 1

sinθ = 1 and cosecθ = 1

sin¹⁵ θ + cosec ¹⁵ θ = (sinθ)¹⁵ + (cosec θ) ¹⁵ = (1)¹⁵ + (1)¹⁵ = 1 + 1 = 2

Q 59) If 1 + sin² θ= 3 sinθ cosθ, then θ =

a) 45^o

b) 30^o

c) 60^o

d) 90^o

Ans: a

Solution Hint

Dividing both side by cos² θ we get

Sec² θ + tan² θ = 3 tan θ

1 + tan² θ + tan² θ = 3 tan θ

2 tan² θ - 3 tanθ + 1 = 0

Factorise this equation we get tan θ = 1 or 1/2

tanθ = 1 ⇒ θ = 45^o

Q 60) If 5 sin θ = 12 cos θ , then find the value of (secθ - tan θ)(secθ + tanθ)

a) 1

b) - 1

c) 2

d) 3

Ans: a

Solution Hint:

(sec θ - tan θ)(sec θ+ tan θ ) = sec² θ – tan² θ = 1

Q 61) If sin θ + cos θ = 1 then what is the value of 3 sin θ cos θ

a) 3

b) 3/ 2

c) 2/ 3

d) 0

Ans: d

Solution Hint

sin θ + cos θ = 1

Squaring on both side and find the value of sin θ cos θ

We get sin θ cos θ = 0 ⇒ 3 x sin θ cos θ = 0

Questions From CBSE Sample Paper 2021-22
Basic Mathematics SP (241)

Q 62) If sinθ = x and secθ = y , then tanθ is

(a) xy

(b) x/y

(c) y/x

(d) 1/xy
Ans: a

Q 63) What is the value of (tanθ cosecθ)² - (sinθ secθ)²

(a) -1

(b) 0

(c) 1

(d) 2
Ans: c

Q 64) Given that sinθ = a/b ,then tanθ is equal to
$a)\: \: \: \frac{b}{\sqrt{a^{2}+b^{2}}}$
$b)\: \: \: \frac{b}{\sqrt{b^{2}-a^{2}}}$

$c)\: \: \: \frac{a}{\sqrt{a^{2}-b^{2}}}$

$d)\: \: \: \frac{a}{\sqrt{b^{2}-a^{2}}}$

Ans: d

Q 65) If x = 2sin²θand y = 2cos²θ+ 1 then x + y is

(a) 3

(b) 2

(c) 1

(d) 1/2
Ans: a

Q 66) If cosθ + cos²θ= 1,the value of sin²θ+ sin⁴θ is

(a) -1

(b) 0

(c) 1

(d) 2

Ans: c

Q 67 In the figure given below, AD = 4cm, BD = 3cm and CB = 12 cm, then cotθ equals

(a) 3/4

(b) 5/12

(c) 4/3

(d) 12/5

Ans: d

Standard Mathematics SP(041)

Q 68 In ∆ABC right angled at B, if tan A= √3, then cos A cos C- sin A sin C =

(a) -1

(b) 0

(c) 1

(d) √3/2

Ans: b

Solution Hint

tan A = √3 = tan 60° so ∠A = 60°, Hence ∠C = 30°.

cos A cos C - sin A sin C = (1/2)x (√3/2) - (√3/2)x (1/2) = 0

Q 69 If the angles of ∆ABC are in ratio 1 : 1 : 2, respectively (the largest angle being angle C), then the value of $\frac{secA}{cosecB}=\frac{tanA}{cotB}$ is

(a) 0

(b) 1/2

(c) 1

(d) √3/2

Ans: a

Solution Hint

1x + 1x + 2x = 180°, x = 45°.

∠A , ∠B and ∠C are 45°, 45° and 90°resp.

Using these values to find the value of the given function.

Q 70 If 4 tanβ = 3, then $\frac{4sin\beta -3cos\beta }{4sin\beta +3cos\beta }=$
(a) 0

(b) 1/3

(c) 2/3

(d) 3 ⁄ 4
Ans: a

Q 71 If tan α + cot α = 2, then tan²⁰α + cot²⁰α =

(a) 0

(b) 2

(c) 20

(d) 2²⁰

Ans: b

Solution Hint

tan α + cot α = 2 gives α = 45°. So tan α = cot α = 1

tan²⁰α + cot ²⁰α = 1²⁰ + 1²⁰ = 1 + 1 = 2

Q 72 If 1+ sin²α = 3 sinα cosα, then values of cot α are

(a) -1, 1

(b) 0, 1

(c)1, 2

(d) -1, -1

Ans: c

Solution Hint

1+ sin²α = 3 sinα cos α

sin²α + cos²α + sin²α = 3 sinα cos α

2 sin²α - 3sinα cos α + cos²α = 0

(2sinα - cos α)( sinα - cosα) =0

⸫ cotα = 2 or cotα = 1

Q 73 If 2sin²β – cos²β = 2, then β is

(a) 0^o (b) 90^o(c) 45^o(d) 30^o

Ans: b

Q 74 In the given figure, D is the mid-point of BC, then the value of $\frac{coty^{o}}{cotx^{o}}$ is

(a) 2 (b) 1/2 (c) 1/3 (d) 1/4

Ans: b

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Maths MCQ Ch-8 Class 10 | Trigonometry

MATHEMATICS MCQ | Class 10 | Chapter 8 TRIGONOMETRY

Questions From CBSE Sample Paper 2021-22Basic Mathematics SP (241)

Standard Mathematics SP(041)

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MATHEMATICS MCQ | Class 10 | Chapter 8
TRIGONOMETRY

Questions From CBSE Sample Paper 2021-22
Basic Mathematics SP (241)