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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 31
Total: 61
sin2x + 2 sin 4x + sin 6x = 4 cos2 x sin 4x
Solution:  
We have,
L.H.S.= sin2x + 2 sin 4x + sin 6x = sin2x + sin 6x + 2 sin 4x
= 2 sin (
2x+6x
2
) cos (
2x−6x
2
) + 2 sin 4x
Since sin A + sin B = 2 sin (
A+B
2
) . cos (
A−B
2
)
= 2sin4x cos(–2x) + 2 sin4x = (2sin4x)(1 + cos (2x)) [Since cos (–θ) = cos θ]
= 2 sin 4x (2 cos2 x) [Since cos2x = 2 cos2 x – 1]
= 4 cos2x sin4x = R.H.S.
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