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Question

State True or False
If x+y+z=π/2, then sin2x+sin2y+sin2z=4cosxcosycosz.

A
True
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B
False
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Solution

The correct option is A True
x+y+z=π2
sin2x+sin2y+sin2z
=2sin(x+y)cos(xy)+2sinzcosz=2cosz(cos(xy)+cos(x+y))
=2cosz(cos(x+y)+cos(xy))
=2cosz2cosxcosy
=4cosxcosycosz
sin2x+sin2y+sin2z=4cosxcosycosz

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