Question

Prove the following identity:
1 + sec^2x sin^2x = sec^2x

Answer 1

\(\bf 1 + sec^2(x) sin^2(x) = sec^2(x)\\
1+ \cfrac{1}{cos^2(x)} sin^2(x) \implies 1+\cfrac{sin^2(x)}{cos^2(x)} \implies 1+tan^2(x)\)

Answer 2

http://www.gradeamathhelp.com/image-files/trigonometric-identities-pythagorean.gif

Answer 3

thank you, you really simplified the problem

Answer 4

yw