Question

Prove that:

1+cot²a / 1 + cosec a = cosec a
​

Answer 1

Explanation:

LHS= 1 + cot^2A/1+cosecA

=(1+cosecA + cot^2A)/1+cosecA

{By using basic trigonometric theorem cot^2A = cosec^2A - 1}

=(1+cosecA + cosec^2A - 1)/(1+cosecA)

=(cosecA + cosec^2A)/(1+cosecA)

=[cosecA (1+cosecA)]/(1+cosecA)

{Cancelling 1+cosecA}

=cosecA