# Trigonometry Questions for SSC CGL 2018 2019, SSC CHSL PDF Download Free at Smartkeeda

Directions : Read the following questions carefully and choose the right answer.
Important for :
1
If 8 sin x = 4 + cos x, the values of sin x are :
» Explain it
D
8 sin x – 4 = cos x ⇒ 8 sin x – 4 =
 1 – sin2 x

⇒ 1 – sin2 x = (8 sin x – 4)2

⇒ 1 – sin2 x = 64 sin2 x + 16 – 64 sin x

⇒ 65 sin2 x – 64 sin x + 15 = 0

⇒ 65 sin2 x – 39 sin x  –  25 sin x + 15 = 0

⇒ 13 sin x (5 sin x  – 3)  –  5 (5 sin x  –  3) = 0

⇒ (5 sin x – 3) (13 sin x – 5) =0

 ⇒ sin x = 3 or sin x = 5 5 13

Hence, option D is correct.

2
If cot ( π  –  Θ )
 3
, then the value of sinΘ – cosΘ = ?
2 2
» Explain it
C
cot ( π  –  Θ )
 3
2 2

 cot ( π – Θ ) = cot 30° 2 2

 or, 90° – Θ = 30° 2

 or, Θ = 60° 2

∴ Θ = 120°

Now, sinΘ – cosΘ = sin120° – cos120°

= sin (90° + 30°) – cos (90°+30°)

= cos 30° + sin 30°

 3
+  1  =
 3 +1
2 2 2

Hence, option C is correct.

3
 If cosΘ = – 1 and π < Θ  < 3π, find the value of 4 tan2Θ – 3 cosec2Θ 2
» Explain it
B
We know that

 sinΘ = ± 1 – cos2Θ

or,  sinΘ  =
 1– 1 4
= –
 3
2

[ Since Θ lies in the third quadrant, value of sinΘ is negative.]

or, cosecΘ  =   –  2
 3

and tanΘ  =  sinΘ  =
 3
cosΘ

[ Since Θ lies in the third quadrant, value of tanΘ is positive.]

 Now, 4 tan2Θ – 3 cosec2Θ = 4 × 3 – 3 × 4 = 8 3

Hence, option B is correct.

4
 The value of sin 300° tan 330° sec 420° is : cot 135° cos 210° cosec 315°
» Explain it
D
 = sin(360° – 60°) tan(360° – 30°) sec(360° + 60°) cot(180° – 45°) cos(180° + 30°) cosec(360° – 45°)

 = ( – sin 60° )( – tan 30°) sec 60° (– cot 45°)(– cos 30°)(– cosec 45°)

= – (
 3
×  1 × 2 )  = –
 2 3
2
 3
1 ×
 3
× 2
2

Hence, option D is correct.

5
If tanΘ + cotΘ = 16, then find the ratio of tan2Θ + cot2Θ to tan2Θ + cot2Θ + 20 tanΘ.cotΘ
» Explain it
D
Given, tanΘ + cotΘ = 16

Squaring both sides, we get

tan2Θ + 2tanΘ cotΘ + cot2Θ = 256

or, tan2Θ + cot2Θ = 256 – 2

∴   tan2Θ + cot2Θ = 254

Now, tan2Θ + cot2Θ + 20tanΘ.cotΘ

 = ( tan2Θ + cot2Θ ) + 20tanΘ . 1 tanΘ

= 254 + 20 = 274

 ∴  Reqd. ratio = 254 = 127 = 127 : 137 274 137

Hence, option D is correct.

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Geometry Questions for SSC 2018 2019 Exams i.e. SSC CGL Tier 1, SSC CHSL, CGL Tier 2

Is it possible to find the height of a tower by merely observing the length of its shadow and the position of the sun? Is it within our powers to deduce the dimensions of a cylindrical container by measuring the height and circumference of the heap of grain that has been poured out of it? One doesn’t need to be a Sherlock Holmes to crack these mysteries. Anyone with an elementary knowledge of geometry will be able to answer these questions. Geometry plays a major role in SSC Exams 2 to 3 questions generally being asked in SSC CGL Tier 1 and SSC CHSL and questions number increased as per the total number of question in particular exams like in SSC CGL Tier 2, that value increased by 5 to 10 questions.
With geometry, one enters, quite literally, into the real world – the world of dimensions. We are not dealing with abstract equations or mere numbers but grappling with concepts like size, shape, location, direction and orientation of objects that figure prominently in real life.

Coordinate geometry and trigonometry find wide applications in varied fields like aviation, defense, navigation and prospecting. Many abstract designs that modern artists and architects create, and we so admire, are nothing more than creatively put together collections of geometric shapes. The concepts of area and perimeter are vital not just to people dealing in real estate but to anyone planning to make optimum use of any available space. As you can see, there is hardly any aspect of the real world that is not influenced by geometry.

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: