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proving a trig identity

+1 vote
(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.
asked Feb 14, 2013 in TRIGONOMETRY by payton Apprentice

1 Answer

+1 vote

LHS image

Even-Odd Identities: cos(-θ) = cosθ

image

Rewrite the expression with common denominator.

image

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

image

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

image

Reciprocal identities: 1/sinθ = cscθ

image  RHS

Therefore  image.

answered Feb 14, 2013 by richardson Scholar

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