Trig functions can’t cancel out in equations; you have to get them on one side and factor it out.

Pythagorean Relationships:
A.) sin^2 θ + cos^2 θ =1
B.) 1 + tan^2 θ = sec^2 θ
C.) 1 + cot^2 θ = csc^2 θ

Reciprocal Relationships:
A.) csc θ = 1/sin θ
B.) sec θ = 1/cos θ
C.) cot θ = 1/tan θ

Steps- (follow loosely)
A.) Algebra
B.) Identities (try Pythagorean theorem, then move everything to sin and cos if that will help)
C.) Algebra
D.) Continue with 1-3 to end of problem

Example 1: sin^2 X – 1

For this problem all you have to do is look at your Pythagorean Relationships and it’s *sin^2 θ + cos^2 θ =1*, so you subtract one and subtract cos^2 X and your answer would be negative cos^2 X.


Example 2: 1 + tan^2 X

For this problem also, all you have to do is look at your Pythagorean Relationships and it’s *1 + tan^2 θ = sec^2 θ*, so your answer is sec^2 X.