proving a trig identity

Question

(1)/(1+cos(-x))+(1)/(1-cos(x))=2csc^2(x) is this an identity? It was a question on the last test I took and I can't see hawto even solve it.

Answer 1

LHS

Even-Odd Identities: cos(-θ) = cosθ

Rewrite the expression with common denominator.

Mathematical formula: (a + b)(a - b) = a² - b²

Pythagorean Identities: sin²θ + cos²θ = 1 ⇒ sin²θ = 1 - cos²θ

Reciprocal identities: 1/sinθ = cscθ

  RHS

Therefore  .