Trigonometry - SSC

From the masthead of a ship of 180 m height to boat, a depression angle of 60 degrees formed. Find out the distance of ship to boat( in m).

• A.

  360

• B.

  60√3

• C.

  180√3

• D.

  180

• View Answer

If A = 30°, what is the value of 

$\frac{8 \sin A+11 \cos ec A-co{t}^{2}A}{10 \cos 2A}$​​​​​​​

• A.

  $5\frac{1}{5}$

• B.

  $4\frac{3}{5}$

• C.

  $4\frac{2}{5}$

• D.

  $3\frac{4}{5}$

• View Answer

If (2 cos A + 1) (2 cos A - 1) = 0, 0° < A ≤ 90°

• A.

  90°

• B.

  45°

• C.

  30°

• D.

  60°

• View Answer

Using the formula tan $\frac{x}{2}$ = $\frac{1-\cos x}{\sin x},$​ find the value of 22.5°.​​​​​​ 

• A.

  $\sqrt{2}$ - 1

• B.

  $\sqrt{2}$ + 1

• C.

  $\frac{\sqrt{3}+\sqrt{2}}{2}$

• D.

  $\frac{\sqrt{3}-\sqrt{2}}{2}$

• View Answer

If sin θ = $\frac{\sqrt{3}}{2},$​​​​​​​ and θ is an acute angle, find the value of cos 3θ.

• A.

  $\frac{1}{2}$

• B.

  1

• C.

  -1

• D.

  0

• View Answer

If $\cos e{c}^2 \theta$ + $co{t}^2\theta$ = $\frac{1}{3},$ Where 0 ≤ θ ≤ $\frac{\pi }{2},$ then the value of $\cos e{c}^4\theta$ - $co{t}^4\theta$ is:

• A.

  $\frac{2}{3}$

• B.

  $-\frac{1}{3}$

• C.

  $\frac{1}{3}$

• D.

  $-\frac{2}{3}$

• View Answer

(tan π + θ) = ?

• A.

  sec θ

• B.

  cosec θ

• C.

  cot θ

• D.

  tan θ

• View Answer

If cosec² θ + cot² θ = $\frac{5}{3}$, then what is value of cot 2θ

• A.

  $\frac{1}{\sqrt{3}}$

• B.

  $-\frac{1}{\sqrt{3}}$

• C.

  $\frac{2}{\sqrt{3}}$

• D.

  $-\frac{2}{\sqrt{3}}$

• View Answer

If tan θ + $\frac{1}{\tan \theta }$ = 2, then the value of tan² θ + $\frac{1}{{\tan }^2\theta }$ is _________.

• A.

  -4

• B.

  2

• C.

  4

• D.

  3

• View Answer

If cosec θ + cot θ = 5, then cosec θ is equal to _________.

• A.

  $\left(5+\frac{1}{5}\right)$

• B.

  $\frac{1}{2}\left(3+\frac{1}{3}\right)$

• C.

  $\frac{1}{2}\left(5+\frac{1}{5}\right)$

• D.

  $\left(3+\frac{1}{3}\right)$

• View Answer

3 sin A - 4 sin³ A = ?

• A.

  cot 3A

• B.

  cos 3A

• C.

  sin 3A

• D.

  tan 3A

• View Answer

The value of sin 2θ (tan θ + cot θ) is:

• A.

  $\frac{2}{3}$

• B.

  1

• C.

  $\frac{1}{2}$

• D.

  2

• View Answer

If sin x - 3 cos x = $\sqrt{3}$ cos x, then the value of cot x

• A.

  3 - $\sqrt{3}$

• B.

  3 + $\sqrt{3}$

• C.

  $\sqrt{3}$

• D.

  $\frac{3-\sqrt{3}}{6}$

• View Answer

If tan θ + cot θ = 4, then find the value of tan²θ + cot²θ.

• A.

  10

• B.

  12

• C.

  16

• D.

  14

• View Answer

The value of $\frac{\sin 4\theta +\sin 2\theta }{\cos 4\theta +\cos 2\theta }$ is:

• A.

  tan 3θ

• B.

  cot 3θ

• C.

  tan θ

• D.

  cot θ

• View Answer

If $\frac{x-x \cos e{c}^2 30°}{1+x \cos e{c}^2 30°}$ = cos 60° + 4 cot 45° - sec 60°, then the value of x is _______.

• A.

  $\frac{5}{12}$

• B.

  $-\frac{5}{12}$

• C.

  $\frac{1}{5}$

• D.

  $-\frac{1}{12}$

• View Answer

If 6 tan A (tan A - 1) = 5 - tan A, Given that O < A < $\frac{\pi }{2}$. What is the value of (sin A + cos A)?

• A.

  3$\sqrt{5}$

• B.

  $\frac{3}{\sqrt{5}}$

• C.

  5$\sqrt{3}$

• D.

  $\frac{5}{\sqrt{3}}$

• View Answer

Simplify the following expression:

cosec⁴ A(1 - cos⁴ A) - 2 cot² A - 1

• A.

  0

• B.

  cos² A

• C.

  cosec² A

• D.

  1

• View Answer

If A = 60°, what is the value of:

$\frac{10 \sin {\displaystyle \frac{A}{2}}+8 \cos A}{7 \sin {\displaystyle \frac{3A}{2}}-12 \cos A}$?

• A.

  9

• B.

  10

• C.

  12

• D.

  7

• View Answer

If 3 sin² θ + 4 cos θ - 4 = 0, 0° < θ < 90°, then the value of (cosec² θ + cot² θ) is

• A.

  $\frac{17}{9}$

• B.

  $\frac{4}{3}$

• C.

  $\frac{25}{3}$

• D.

  $\frac{5}{4}$

• View Answer

If A = 60°, what is the value of:

$\frac{\left[8 \cos A+7 sec A-{\tan }^{2}A\right]}{10 \sin {\displaystyle \frac{A}{2}}}$

• A.

  5

• B.

  3

• C.

  15

• D.

  10

• View Answer

If sec² θ + tan² θ = 3$\frac{1}{2}$, 0° < θ < 90°, then (cos θ + sin θ) is equal to

• A.

  $\frac{1+\sqrt{5}}{3}$

• B.

  $\frac{2+\sqrt{5}}{3}$

• C.

  $\frac{1+\sqrt{5}}{6}$

• D.

  $\frac{9+2\sqrt{5}}{6}$

• View Answer

Find the value of the following expression:

$\frac{{\tan }^3 45° + 4 {\cos }^3 60°}{2 \cos e{c}^2 45°-3 se{c}^2 30° + \sin 30°}$

• A.

  1 + $\sqrt{2}$

• B.

  $\frac{4}{3}$

• C.

  $\frac{3}{4}$

• D.

  3

• View Answer

If 3 sec² θ + tan θ - 7 = 0, 0° < θ < 90°, then what is the value of $\left(\frac{2 \sin \theta +3 \cos \theta }{\cos ec + sec \theta +sec \theta }\right)$

• A.

  10

• B.

  $\frac{5}{2}$

• C.

  $\frac{5}{4}$

• D.

  4$\sqrt{2}$

• View Answer

If cot B = $\frac{12}{5}$, what is the value of sec B

• A.

  $\frac{5}{12}$

• B.

  $\frac{13}{12}$

• C.

  $\frac{13}{5}$

• D.

  $\frac{12}{13}$

• View Answer