Question

Simplify this trig. expression:

Answer 1

\[\sec x \sqrt{\frac{ (1- \sin^2 y)(\sin^2x) }{ (1+\cos^2y)(\tan^2x) }}\]

Answer 2

\[\sec x \sqrt\frac{(1-\sin^2 y)(\sin^2 x)}{(1+\cos^2 y)(\tan^2 x)}=\frac{1}{\cos x}\sqrt\frac{(\cos^2 y)(\sin^2 x)}{(1+\cos^2 y)(\tan^2 x)}\]\[=\frac{1}{\cos x}\frac{(\cos y)(\sin x)}{\sqrt{1+\cos^2 y}(\tan x)}\][Can you do the cancellation for the rest?]

Answer 3

Do you mind showing one more step?