NCERT Class XI Mathematics - Trigonometric Functions - Solutions
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Question : 58
Total: 61
ain 3x + sin 2x - sin x = 4 sin x cos
Solution:
We have,
L.H.S.= sin 3x + sin 2x – sinx = sin 3x – sin x + sin 2x
= 2 cos(
) s i n (
)
Since sin A - sin B = 2 cos(
) s i n (
)
= 2cos(2x) sinx + 2 sinx cosx [Since sin 2x = 2 sinx cosx]
= 2 sinx [cos 2x + cosx]
= 2 sin x[ 2 c o s (
) c o s ( 2 x −
) ]
Since cos A + cos B = 2 cos(
) (
)
= 2 sin x 2 cos
c o s
L.H.S.= sin 3x + sin 2x – sinx = sin 3x – sin x + sin 2x
= 2 cos
Since sin A - sin B = 2 cos
= 2cos(2x) sinx + 2 sinx cosx [Since sin 2x = 2 sinx cosx]
= 2 sinx [cos 2x + cosx]
= 2 sin x
Since cos A + cos B = 2 cos
= 2 sin x 2 cos
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