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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 53
Total: 61
(sin 3x + sinx) sin x + (cos3x – cosx) cosx = 0
Solution:  
We have, L.H.S.= (sin3x + sinx) sinx + (cos3x – cosx) cosx
= (2sin(
3x+x
2
)cos(
3x−x
2
) sin x + (−2sin(
3x+x
2
)sin(
3x−x
2
)) cos x
Since sin A + sin B = 2 sin (
A+B
2
) cos (
A−B
2
)
and
cos A - cos B = - 2 sin (
A+B
2
) cos (
A−B
2
)
= [(2 sin2x cosx) sinx] – [(2 sin2x sinx) cosx]
= [2 sin2x sinx cosx – 2 sin2x·sinx cosx] = 0 = R.H.S.
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