Question

(sin 3x)(sin 4x) = 1/2(cos x- cos 7x) please prove it!​

Answer 1

Step-by-step explanation:

2 sin a sin b = cos ( a - b ) - cos ( a + b ) where a < b

so, 2 sin 3x sin 4x = cos (3x - 4x) - cos ( 3x + 4x)

Thus ,

sin 3x sin 4x = ½ ( cos x - cos 7x )

Note that cosine is even function.....

Hope it will help you

Answer 2

Answer:

2 Sin A . Sin B = Cos ( A-B) x - Cos ( A + B ) x

consider

Sin 3x . Sin 4x

multiplying and dividing by 2

1/2 ( 2 sin3x. sin4x )

1/2 ( cos ( 3x-4x) - cos( 3x + 4x )

1/2 ( cos ( -x) - cos 7x )

1/2 ( cos x - cos 7x )

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