NCERT Class XI Mathematics - Trigonometric Functions - Solutions
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Question : 27
Total: 61
sin(n + 1)x sin(n + 2)x + cos(n + 1)x cos(n + 2)x = cos x
Solution:
We have, L.H.S.= sin (n + 1)x sin (n + 2) x + cos (n + 1)x cos(n + 2) x
= cos ((n + 1) x – (n + 2) x) [Since cos (A – B) = cos A cos B + sin A sin B]
= cos((n + 1 – n – 2) x) = cos (– x) = cos x = R.H.S.
= cos ((n + 1) x – (n + 2) x) [Since cos (A – B) = cos A cos B + sin A sin B]
= cos((n + 1 – n – 2) x) = cos (– x) = cos x = R.H.S.
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