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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 38
Total: 61
cos4x+cos3x+cos2x
sin4x+sin3x+sin2x
 = cot 3x
Solution:  
We have, L.H.S.=
cos4x+cos3x+cos2x
sin4x+sin3x+sin2x
=
2cos(
4x+2x
2
)cos(
4x−2x
2
)+cos3x
2sin(
4x+2x
2
)cos(
4x−2x
2
)+sin3x

=
2cos3xcosx+cos3x
2sin3xcosx+sin3x
 =
cos3x(2cosx+1)
sin3x(2cosx+1)
 =
cos3x
sin3x
 = cot 3x = R.H.S.
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