convert the following product into sum or differences 1)2sin3xcosx 2)2cos7xcos3x
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Answer:
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Answer:
1) 2 sin 3x cos x = sin 4x + sin 2x
2) 2 cos 7x cos 3x = cos 10x + cos 4x
Step-by-step explanation:
1. 2 sin 3x cos x
We know that 2 sin A cos B = sin (A + B) + sin (A - B)
Here, let us take 3x as A and x as B
=> 2 sin 3x cos x = sin (3x + x) + sin (3x - x)
= sin 4x + sin 2x
which is the required answer. i.e. in sum form
Therefore, 2 sin 3x cos x = sin 4x + sin 2x
2. 2 cos 7x cos 3x
We know that 2 cos A cos B = cos (A + B) + cos (A - B)
Here, let us take 7x as A and 3x as B
=> 2 cos 7x cos 3x = cos (7x + 3x) + cos (7x - 3x)
= cos 10x + cos 4x
which is the required answer. i.e. in sum form
Therefore, 2 cos 7x cos 3x = cos 10x + cos 4x