SSC CGL 2022 PYQ — Question 51

The correct answer is Option 2 i.e. cosec A + cot A.

Concept USed:

$\sin^2 A = 1 - \cos^2A$

1/sinA = cosecA

cosA/sinA = cotA

Explanation:

Multiplying (1 + cosA) in both numerator and denominator of $\sqrt{{1+cosA} \over 1-cosA}$ , 

we get

⇒ ${\sqrt{{(1 + cosA)(1 + cosA) }\over {(1 - cosA)(1 + cosA)}}}$ = $\sqrt{(1+cosA)^2 \over {1 - cos^2A}}$ = $\sqrt{(1 + cosA)^2 \over sin^2A}$

Removing square root, $(1 + cosA)\over sinA$ = ${1 \over sinA} + {cosA \over sinA}$ = cosecA + cotA.

Hence the value of$\sqrt{{1+cosA} \over 1-cosA}$ = cosecA + cotA.