# Proving a trigonometric identity and solving for theta (two questions)

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• Aug 7th 2013, 11:11 PM
Coshy
Proving a trigonometric identity and solving for theta (two questions)
Hi guys,

How would one prove the following trigonometric identity.

sinθ(1 + tanθ) + cosθ(1 + cotθ) = sinθ+cosθ / sinθcosθ

Also, how would one find the value of cosθ and also cos(2θ) if sinθ = 3/5 and Pi/2 < θ < pi

Thanks in advance for any help :).
• Aug 8th 2013, 12:24 AM
ShadowKnight8702
Re: Proving a trigonometric identity and solving for theta (two questions)
For the first problem, remember that sin^2 θ + cos^2 θ = 1.
First distribute, and then put every term over sinθcosθ. Group the terms in such a way that you can create sin^2 θ + cos^2 θ by factoring. You will end up with (sinθ+cosθ) / sinθcosθ.

For the second problem, recognize that sinθ = 3/5 is giving you two out of the three sides of a triangle, and with pythagorean theorem you can easily find the third side. Pi/2 < θ < pi gives you the quadrant. From there, just plug in.