Simplify sin^2x/sec^2x-1

Question

Verify the identity

Answer 1

sin²x/sec²x-1

sin²x/(1/cos²x)-1

sin²x/(1/cos²x)-(cos²x/cos²x)

sin²x/[(1-cos²x)]/[cos²x]

sin²xcos²x/(1-cos²x)

sin²xcos²x/sin²x because sin²x+cos²x=1

cancel the sin²x's

cos²x is the simplest form