Question

Verify Identities:
sec²a=1/1-sin²a​

Answer 1

Answer:  see proof below

Explanation:

$sec^2\alpha=\dfrac{1}{1-\sin^2 \alpha}$

LHS → RHS

$sec^2\alpha\qquad \text{Given}\\\\\dfrac{1}{cos^2\alpha}\qquad \text{sec is reciprocal of cos}\\\\\\\dfrac{1}{1-sin^2\alpha}\qquad \text{Identity}:cos^2\alpha + sin^2\alpha = 1\\\\\\\dfrac{1}{1-sin^2\alpha}=\dfrac{1}{1-sin^2\alpha}\quad \checkmark$