Question

Verify the trigonometric identity:
[(1–sin²x)/sin²x]–[(csc²x–1)/cos²x]=
-tan²x

I still can't figure this out.

Answer 1

Solve the equation by multiplying, adding, dividing, and subtracting where neccessary. Keep in mind your constants and like terms. Also remember, identity is another way of saying "two sides of an equation that are equal to each other". For example, 2x+0=2x would be identity.

Answer 2

check your typing, since I can prove that your Left Side = -1

L.S. = [(1–sin²x)/sin²x]–[(csc²x–1)/cos²x]
= cos²x/sin²x - cot²x/cos²x
= cos²x/sin²x - 1/sin²x
= (cos²x - 1)/sin²x
= -sin²x/sin²x
= -1