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# Prove

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No longer require the answer to this, but if you want to, feel free to try it so I can double check my math (but also my newest question is more urgent).

Prove this identity:

$$1-8sin^2\theta cos^2\theta=cos(4\theta)$$

May 15, 2019
edited by AdamTaurus  May 15, 2019
edited by AdamTaurus  May 15, 2019

$$1-8sin^2\theta cos^2\theta=cos(4\theta)\\ LHS=1-2(2sin\theta cos\theta)^2\\ LHS=1-2sin^2(2\theta)\\ LHS=1-sin^2(2\theta)-sin^2(2\theta)\\ LHS=cos^2(2\theta)-sin^2(2\theta)\\ LHS=cos(4\theta)\\ LHS=RHS \qquad\\ QED$$