# Trigonometry Questions with Solution for SSC CGL, MTS, CHSL with PDF at Smartkeeda

Direction: Study the following questions carefully and choose the right answer:
Important for :
1
The value of  (sin 39°) / (cos 51°)  +  2 tan11° tan31° tan45° tan59° tan79°  –  3 (sin2 21° + sin2 69°) is :
» Explain it
D
(sin 39°) / (cos 51°)  +  2 tan11° tan31° tan45° tan59° tan79°  –  3 (sin2 21° + sin2 69°)

(sin 39°) / (sin 39°)  +  2 tan 11° cot 11° tan 31° cot 31° tan 45° – 3(sin2 21° + cos2 21°)

[∵  cos (90° – Θ) = sin Θ, tan (90° – Θ) = cot Θ   &   sin (90° – Θ) = cos Θ]

= 1 + 2 × 1 × 1 × 1 – 3 × 1

[  ∵  tan Θ cot Θ = 1, tan 45° = 1    &    sin2 Θ + cos2 Θ = 1  ]

= 1 + 2 – 3 = 0

Hence, option D is correct.

2
If  cos2 Θ  /  (cot2 Θ – cos2 Θ)   = 3 and 0° < Θ < 90°, then the value of Θ is :
» Explain it
C
 cos2 Θ = 3 cot2 Θ – cos2 Θ

⇒ cos Θ = 3 cot Θ – 3 cos Θ

 ⇒ 4 cos Θ = 3 cos Θ sin Θ

⇒ 4 sin Θ = 3

 ⇒ sin Θ = 3 4

⇒ sin Θ =
 3
= sin 60°
2

⇒ Θ = 60°

Hence, option C is correct.

3
If A = tan 11° tan 29°, B = 2 cot 61° cot 79°, then :
» Explain it
C
Given, A = tan 11° tan 29°

And, B = 2 cot 61° cot 79°

Or, B = 2 tan 29° tan 11° = 2A

[∵  cot (90° – Θ) = tan Θ]

So, 2A = B.

Hence, option C is correct.

4
If sin 17° = x / y, then the value of (sec 17° – sin 73°) is
» Explain it
B
 Given, sin 17° = x y

 sec 17° – sin 73° = 1 – sin (90° – 17°) cos 17°

 [ ∵ sec Θ = 1 ] cos Θ

 = 1 – cos 17° cos 17°

 [ ∵ sin (90° – Θ) = cos Θ ]

 = 1 – cos2 17° cos 17°

 = sin2 17° 1 – sin2 17°

[∵ 1 – cos2 Θ = sin2 Θ & cos Θ = 1 – sin2 Θ ]

 x2 y2
 1 – x2 y2

 x2 y2
=
x2
 y y2 – x2
 y2 – x2
y

Hence, option B is correct.

5
 The expression tan 57° + cot 37° is equal to tan 33° + cot 53°
» Explain it
B
 tan 57° + cot 37° tan 33° + cot 53°

 = tan (90° – 33°) + cot (90° – 53°) tan 33° + cot 53°

 = cot 33° + tan 53° tan 33° + cot 53°

[ ∵ tan (90° – Θ) = cot Θ  &  cot (90° – Θ) = tan Θ ]

 1 + tan 53° tan 33°
 tan 33° + 1 tan 53°

[ ∵ cot Θ =
 1 tan Θ
]

 1 + tan 53° tan 33° tan 33°
 tan 33° tan 53° + 1 tan 53°

 = tan 53° = cot 33° tan 53° tan 33°

 [ ∵ 1 = cot Θ ] tan Θ

= cot (90° – 57°) tan (90° – 37°)

= tan 57° cot 37°

[∵ cot (90° – Θ) = tan Θ  &  tan (90° – Θ) = cot Θ]

Hence, option B is correct.