Verify:

Question

1/(1-sintheta) * 1/(1+sintheta) = sec^2theta

Answer 1

=[1/(1-sin x)]*[1/1+sin x]
=1/(1-sin x)*(1+sin x)
=1/1-(sin x)^2 :using Pythagorean identity
=1/(cos x)^2 :using reciprocal identity
=(sec x)^2