When trying to prove trig identities, it is often helpful to convert TAN functions into SIN/COS functions:

**Proof Step 1**: Start with the original equation to prove:

tan^{2}x - sin^{2}x = (tan^{2}x)(sin^{2}x)

**Proof Step 2**: Replace tan with sin/cos

(sin^{2}x/cos^{2}x) - sin^{2}x = (sin^{2}x/cos^{2}x)(sin^{2}x)

**Proof Step 3**: Obtain a common denominator on left, simplify right

(sin^{2}x - sin^{2}x cos^{2}x) / cos^{2}x = sin^{4}x / cos^{2}x

**Proof Step 4**: Cancel cos^{2}x from both denominators

sin^{2}x - sin^{2}x cos^{2}x = sin^{4}x

**Proof Step 5**: Factor out sin^{2}x from left

(sin^{2}x)(1 - cos^{2}x) = sin^{4}x

**Proof Step 6**: Use trig identity 1-cos^{2}x = sin^{2}x

(sin^{2}x)(sin^{2}x) = sin^{4}x

**Proof Step 7**: Simplify, DONE.

sin^{4}x = sin^{4}x

Lauren L.

Could you remind me how you factored out sin^2x from the left in proof step 5? Other than that, everything else was very helpful, it makes so much more sense.

11/18/12