Q. 95.0( 9 Votes )

# Prove that sin 4A

Answer :

sin 4A = sin (2A + 2A)

As we know that-

sin(A + B) = sin A cos B + cos A sin B

sin 4A = sin 2A cos 2A + cos 2A sin 2A

sin 4A = 2 sin 2A cos 2A

From T-ratios of multiple angle, we know that

sin 2A = 2 sin A cos A and cos 2A = cos2A – sin2A

sin 4A = 2(2 sin A cos A)(cos2A – sin2A)

sin 4A = 4 sin A cos3A – 4 cos A sin3A

Hence: sin 4A = 4 sin A cos3A – 4 cos A sin3A

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