NIMCET 2017 Question Paper with solutions

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Question : 90 of 120

Marks: +1, -0

Express (cos5x - cos7x) as a product of sines or cosines or sines and cosines.

2cos4xcosx
2 sin 4x sin x
2sin6xsinx
2 cos 6x cos x

Solution:

We know that,
cos C - cos D = 2 sin

({C+D}/2)sin({D-C}/2)

∴ cos 5 x - cos 7x = 2 sin

({5x+7x}/2)sin({7x-5x}/2)

= 2 sin

({12x}/2)

sin

({2x}/2)

= 2 sin 6x sinx

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