Michael J. answered • 12/14/16

Understanding all Sines of Triangles

^{2}θ) =

^{2}θ =

^{2}θ) =

^{2}θ =

Frannie E.

asked • 12/14/16I have a math problem in which I have to prove the identity sin2θ= 2tanθ/1+tan^{2}θ using Double-Angle Identities and I'm trying to figure out how to solve it.

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Michael J. answered • 12/14/16

Tutor

5
(5)
Understanding all Sines of Triangles

Simplify the right side.

2tanθ / (1 + tan^{2}θ) =

2tanθ / sec^{2}θ =

2(sinθ/cosθ) / (1/cos^{2}θ) =

2(sinθ/cosθ) * cos^{2}θ =

2sinθcosθ

The identity is true.

Hilton T.

tutor

Michael,

Please check the identity. In the identity for tan (2theta), there should be a negative sign (not a positive sign) in the denominator.

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12/15/16

Michael J.

The student made an error in the question title. I went with the detailed description:

Prove sin2θ = 2tanθ/(1+tan^{2}θ)

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12/16/16

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Michael J.

12/15/16