How do you prove # (cos(x/2)-sin(x/2))^2= 1-sinx#?

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Answer 1 · 2016-04-17T04:19:00

See below

Use Properties:
#sin^2x+cos^2x=1, and sin2x=2sinxcosx#

Left Side #=cos^2(x/2)-2sin(x/2)cos(x/2)+sin^2(x/2)#

#=cos^2(x/2)+sin^2(x/2)-2sin(x/2)cos(x/2)#

#=1-2sin(x/2)cos(x/2)#

#=1-sin(2(x/2))#

#=1-sinx#

#=#Right side