Trigonometry Important Questions Set-2 for SSC CGL Exam

By | February 2, 2018

Trigonometry Important Questions Set-2 for SSC CGL Exam

  1. A ladder is resting against a wall at height of 10m. If the ladder is inclined with the ground at an angle of 30°, then the distance of the foot of the ladder from the wall is

(a) 10\sqrt { 3 } m
(b) 20\sqrt { 3 } m
(c) \frac { 10 }{ \sqrt { 3 } } m
(d) \frac { 20 }{ \sqrt { 3 } } m

Answer : (a) 10\sqrt { 3 } m
Explanation : Let 'x' be the distance of foot of ladder

tan 30° = \frac { P }{ B } = \frac { 10 }{ X }

\Rightarrow \frac { 10 }{ \sqrt { 3 } } = \frac { 10 }{ X }

\Rightarrow x = 10\sqrt { 3 } m

  1. tan 7° tan 23° tan 60° tan 67° tan 83 is equal to
    (a) \frac { 1 }{ \sqrt { 3 } }
    (b) 1
    (c) 0
    (d) \sqrt { 3 }

Answer: (d) \frac { 3 }{ 2 }

Explaination: tan 7° tan 23° tan 60° tan 67° tan 83°

= tan (90° - 83°)tan (90° - 67°)tan 60° X tan 67° X tan 83°
= Cot 83° X Cot 67° X tan 60° tan 67° tan 83°
= \frac { 1 }{ tan 83^{\circ} } X \frac { 1 }{ tan 67^{\circ}} X tan 60° X tan 67° X tan 83°
= tan 60°
= \sqrt { 3 }

3.The value of (sec 0 - cos 0)(cosec 0 - sin 0)(tan 0 + cot 0) is
(a) 2
(b) 0
(c) 1
(d) \frac { 3 }{ 2 }
Answer : (c) 1
Explaination :
(sec 0 - cos 0)(cosec 0 - sin 0)(tan 0 + cot 0)
= \left( \frac { 1 }{ Cos\theta } -\quad Cos\theta \right) \left( \frac { 1 }{ Sin\theta } -\quad Sin\theta \right) \left( \frac { Sin\theta }{ Cos\theta } +\frac { Cos\theta }{ Sin\theta }\right)
= \left( \frac { 1-{ Cos }^{ 2 }\theta }{ Cos\theta } \right) X \left( \frac { 1-{ Sin }^{ 2 }\theta }{ Sin\theta } \right)
= \frac { { Sin }^{ 2 }\theta +{ Cos }^{ 2 }\theta }{ Sin\theta Cos\theta }
= \frac { { Sin }^{ 2 }\theta }{ Cos\theta } \times \frac { { Sin }^{ 2 }\theta }{ Cos\theta } \times \frac { 1 }{ Sin\theta \quad Cos\theta }

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