Trigonometry Identity

Question

Please fully complete this identity, step-by-step with as much detail as necessary!

(Note: 'θ' (theta) just means angle. It can be replaced with 'x'.)

Prove that (cos θ - tan θ)² - 2 ≡ tan² θ - (1 + sin θ)²

Answer 1

cos² - 2 cos tan + tan² - 2 = 1 - sin² - 2 sin + tan² -2 = tan² - sin² -2 sin -1=tan² - (1 + sin)²