SSC CGL 2024 PYQ — Question 70

The correct answer is option 4 i.e. 1.

⇒ $\tan(4\theta) \cdot \tan(6\theta) = 1$

⇒ $\tan(4\theta) \cdot \tan(6\theta) = 1$

$\tan(A) \cdot \tan(B) = 1$

A + B = 90°

⇒ $4\theta + 6\theta = 90^\circ$

⇒ $10\theta = 90^\circ$

⇒ $\theta = \frac{90^\circ}{10} = 9^\circ$

$\theta = 9^\circ$  , we can compute $( 5\theta)$:

⇒ $5\theta = 5 \times 9^\circ = 45^\circ$

The cotangent of ( 45° ) is:

⇒ cot(45° ) = 1

The value of $( \cot(5\theta) )$ is: 1 .