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Question: \(\sin 4\theta\)can be written as...

sin⁡4θ\sin 4\thetacan be written as

A

4sin⁡θ(1−2sin⁡2θ)1−sin⁡2θ4\sin\theta(1 - 2\sin^{2}\theta)\sqrt{1 - \sin^{2}\theta}

B

2sin⁡θcos⁡θsin⁡2θ2\sin\theta\cos\theta\sin^{2}\theta

C

4sin⁡θ−6sin⁡3θ4\sin\theta - 6\sin^{3}\theta

D

None of these

Answer

4sin⁡θ(1−2sin⁡2θ)1−sin⁡2θ4\sin\theta(1 - 2\sin^{2}\theta)\sqrt{1 - \sin^{2}\theta}

Explanation

Solution

sin⁡4θ=2sin⁡2θcos⁡2θ\sin 4\theta = 2\sin 2\theta\cos 2\theta

=2.2sin⁡θcos⁡θ(1−2sin⁡2θ)= 2.2\sin\theta\cos\theta(1 - 2\sin^{2}\theta)

=4sin⁡θ(1−2sin⁡2θ)1−sin⁡2θ= 4\sin\theta(1 - 2\sin^{2}\theta)\sqrt{1 - \sin^{2}\theta}