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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 37
Total: 61
sinx−sin3x
sin2x−cos2x
 = 2 sin x
Solution:  
We have, L.H.S.=
sinx−sin3x
sin2x−cos2x
 =
2cos(
x+3x
2
)sin(
x−3x
2
)
−(cos2x−sin2x)
=
2cos2xsin(−x)
−cos2x
 [Since cos2x−sin2 x = cos 2x]
=
−2sinx
−1
 [Since sin (θ) = - isn θ] = sin x = R.H.S.
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