Sin^2x-tan^2x=-sin^2xtan^2x

Question

Trigonometric identities and proof

Answer 1

Since tan²x =sin²x/cos²x, we can replace tan²x with it to get

Sin²x-sin²x/cos²

Then factor out sin²x to get 

Sin²x(1  - 1/cos²x).

1/cos x = sec x, so by substitution, we get

Sin²x(1 - sec²x)

Now 1 - sec²x = tan²x, so by replacement we are left with

Sin²x tan²x.