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# P2 trig proof question watch

1. Ive done this question about 10 times, and still cant prove it. Ive looked at the answers and just dont understand them.

Prove that:
2tanx - sin2x = 2sin^2x.tanx
2. (Original post by BlueAngel)
Ive done this question about 10 times, and still cant prove it. Ive looked at the answers and just dont understand them.

Prove that:
2tanx - sin2x = 2sin^2x.tanx
2tanx-sin2x=2tanx-2sinxcosx
=2sinx/cosx-2sinxcosx
=(2sinx-2sinxcos^2x)/cosx [times top and bottom by cosx]
=tanx(2-2cos^2x) [sinx/cosx=tanx ]
=tanx(2-2(1-sin^2x) [sin^2x=1-cos^2x]
=tanx(2+2sin^2x-2)
=tanx(2sin^2x)
3. On the right, make sin^2 = 1-cos^2, so you get
2sin^2xtanx = (2 - 2cos^2x)tanx = 2tanx - 2cosxsinx = 2tanx - sin2x
4. thank you all.

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Updated: June 19, 2004
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