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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 55
Total: 61
(cosx−cosy)2 + (sinx−siny)2 = 4cos2
x−y
2
Solution:  
We have,
L.H.S.= (cosx−cosy)2 + (sinx−siny)2
= [−2sin(
x+y
2
)sin(
x−y
2
)]2 + [2cos(
x+y
2
)sin(
x−y
2
)]2
= 4sin2(
x+y
2
)sin2(
x−y
2
) + 4cos2(
x+y
2
)sin2(
x−y
2
)
= 4sin2(
x−y
2
) [sin2(
x+y
2
)+cos2(
x+y
2
)]
= 4sin2(
x−y
2
) = R.H.S.
Since sin2x+cos2x = 1
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