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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 57
Total: 61
(sin7x+sin5x)+(sin9x+sin3x)
(cos7x+cos5x)+(cos9x+cos3x)
Solution:  
We have,
L.H.S. =
(sin7x+sin5x)+(sin9x+sin3x)
(cos7x+cos5x)+(cos9x+cos3x)
2sin(
7x+5x
2
)cos(
7x−5x
2
)
=
+2sin(
9x+3x
2
)cos(
9x−3x
2
)
2cos(
7x+5x
2
)cos(
7x−5x
2
)
+ 2cos(
9x+3x
2
)cos(
9x−3x
2
)
Since cos A + cos B = 2 cos (
A+B
2
)cos(
A−B
2
)
sin A + sin B = 2 sin (
A+B
2
)cos(
A−B
2
)
=
2sin6xcosx+2sin6xcos3x
2cos6xcosx+2cos6xcos3x
 =
2[cosx+cos3x]sin6x
2[cosx+cos3x]cos6x]
=
sin6x
cos6x
 = tan 6x = R.H.S.
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