SSC CGL 2022 PYQ — Question 72

The correct answer is Option 4 i.e. 2cot 2x.

Concept Used:

cosecx = 1/sinx

secx = 1/cosx

tanx = 1/cotx

sinx/cosx = tanx

cosx/sinx = cotx

$cot2x = {{cot^2x -1} \over 2cotx}$

Explanation:

From the given question, we have

cos x cosec x – sin x sec x = cosx/sinx - sinx/cosx

⇒ cotx - tanx

⇒ cotx - 1/cotx

⇒ ${cot^2x - 1} \over cotx$

Now, multiplying numerator and dinominator by 2, we get

⇒ $2{cot^2x - 1}\over 2cotx$ = 2cot2x.

Hence the value of cos x cosec x – sin x sec x is 2cot2x.