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

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