It's trigo time #10

Geometry Level 1

Simplify

1 − cos ⁡ 2 θ 2 \large \frac{1-\cos2\theta }{2}

Prove your answer.

cos ⁡ θ \cos\theta cot ⁡ θ \cot\theta sin ⁡ 2 θ \sin^2\theta tan ⁡ θ \tan\theta

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Chew-Seong Cheong
May 19, 2017

1 − cos ⁡ 2 θ 2 = 1 − ( 1 − 2 sin ⁡ 2 θ ) 2 = 2 sin ⁡ 2 θ 2 = sin ⁡ 2 θ \begin{aligned} \frac {1-\cos 2\theta}2 & = \frac {1-(1-2\sin^2 \theta)}2 \\ & = \frac {2\sin^2 \theta}2 \\ & = \boxed{\sin^2 \theta} \end{aligned}

4 Helpful 0 Interesting 1 Brilliant 0 Confused

That's the solution that I wanted thank you sir

Biswajit Barik - 4 years ago

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