# 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) $\frac { 3 }{ 2 }$
= $\left( \frac { 1 }{ Cos\theta } -\quad Cos\theta \right)$ $\left( \frac { 1 }{ Sin\theta } -\quad Sin\theta \right)$ $\left( \frac { Sin\theta }{ Cos\theta } +\frac { Cos\theta }{ Sin\theta }\right)$
= $\left( \frac { 1-{ Cos }^{ 2 }\theta }{ Cos\theta } \right)$ X $\left( \frac { 1-{ Sin }^{ 2 }\theta }{ Sin\theta } \right)$
= $\frac { { Sin }^{ 2 }\theta +{ Cos }^{ 2 }\theta }{ Sin\theta Cos\theta }$
= $\frac { { Sin }^{ 2 }\theta }{ Cos\theta } \times \frac { { Sin }^{ 2 }\theta }{ Cos\theta } \times \frac { 1 }{ Sin\theta \quad Cos\theta }$