 # Trigonometry Questions and Answers for Competitive Exams Like CGL, CHSL, MTS at Smartkeeda

Important for :
1
Find the value of sin2 10 + sin2 20 + sin2 30 + ....... + sin2 80.
» Explain it
D
We can rewrite above equation as

sin2 10 + sin2 80 + sin2 20 + sin2 70 + sin2 30 + sin2 60 + sin2 40 + sin2 50   ….. equation (A)

We know that sin2 x + sin2 (90 – x) = 1

Therefore equation A becomes

1 + 1 + 1 + 1 = 4

Hence, option D is correct.

2
Find the value of 16/ 3 (Cos50°Cos10°Cos110°Cos60°)
» Explain it
C
We have cos x cos (60 – x ) cos (60 + x )

= cos x (cos x cos 60 + Sin x Sin 60°) (cos x cos 60° – Sin x Sin 60°)

= cos x (cos2x cos260° – Sin2x Sin260°)

 = cos x ( 1 cos 2 – 3 sin2 x ) 4 4

 = 1 { cos 3 x – 3 cos x (1 – cos 2 x ) } 4

 = 1 (4 cos 3 x – 3 cos x ) 4

 = 1 cos 3 x 4

Thus,

 cos x ° cos (60 – x )° cos (60 + x ) = 1 cos (3 x ) 4

Therefore,
 cos 50° cos 10° cos 110° = 1 cos 150° 4

 = 1 (–√3/2) = – √3 ... eq A 4 8

 Also cos 60° = 1 ... eqB 2

Put values of eq.A and Eq.B in

 16 (cos 50°cos 10cos 110°cos 60°), we get √3

 = 16 × ( – √3 ) × 1 √3 8 2

= – 1

Option C is hence the correct answer.

3
Find the value of

cos2 Θ  (
 1 + sin Θ 1 – sin Θ
+
 1 – sin Θ 1 + sin Θ
)
» Explain it
C
cos2 Θ  (
 (1 + sin Θ) (1 + sin Θ) (1 – sin Θ) (1 + sin Θ)
+
 (1 – sin Θ) (1 – sin Θ) (1 + sin Θ) (1 – sin Θ)
)

⇒ cos2 Θ  (
 (1 + sin Θ)2 (1 – sin2 Θ)
+
 (1 – sin Θ)2 (1 – sin2 Θ)
)

⇒ cos2 Θ  (
 (1 + sin Θ)2 cos2 Θ
+
 (1 – sin Θ)2 cos2 Θ
)

 ⇒ cos2 Θ ( 1 + sin Θ + 1 – sin Θ ) cos Θ cos Θ

 ⇒ cos2 Θ ( 1 + sin Θ + 1 – sin Θ ) cos Θ

 2 cos2 Θ = 2 cos Θ cos Θ

Hence, option C is correct.

4
If sin 21° = x/y, then sec 21° – sin 69° is equal to
» Explain it
A
 Sin 21° = x y

Cos 21°= ((1 – (sin 21°)2 )
⇒
 1 – x2 y2
=  √(y2 – x2)
y

 ⇒ sec 21 ° = y √(y2 – x2)

According to the question,

⇒ sec 21°– sin⁡ 69°

⇒ sec⁡ 21°– sin⁡ (90– 21°)

⇒ sec⁡ 21° – cos⁡21°
 ⇒ y – √(y2 – x2) √(y2 – x2) y

 ⇒ x2 y √(y2 – x2)

Hence, option A is correct.
5
Find the value of :

 ( sin 35° ) 2 + ( cos 55° ) 2 – 2 cos 30° cos 55° sin 35°

» Explain it
C
 ( sin 35° ) 2 + ( cos 55° ) 2 – 2 cos 30° cos 55° sin 35°

 ⇒ ( sin (90 – 35°) ) 2 + ( cos (90 – 55°) ) 2 – 2 cos 30° cos 55° sin 35°

 ⇒ ( cos 55 ° ) 2 + ( sin 35° ) 2 – 2 cos 30° cos 55° sin 35°

 ⇒ 1 + 1 – 2 × √3 2
⇒ 2 – √3

Hence, option C is correct.

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### Trigonometry Questions for Competitive Exams with PDF like SSC CGL Tier 1, CHSL, MTS, CGL Tier 2

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At Smartkeeda you familiarized yourself with the key concepts and improved your problems-solving abilities. Practice and tests are important to optimize your preparation. Take the tests on Testzone to improve your problem-solving skills. Questions that have appeared in the previous SSC CGL and SSC CHSL exams are also in the given quizzes. Through them you can understand where the focus lies in an examination environment. The detailed solutions and short tricks of the questions may provide some alternate strategies that can help you improve your speed accuracy. You can practice individual exercise practice and you can analyze yourself topic wise as Trigonometry, Height and Distance, Quadrilateral and Polygon, Triangle, Circle, and Lines and Angles. Here are some Important Geometry Chapters Links: