Question 882956
Hello!
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Since the right side is more complicated, let us work from the right and try to get to the left side.
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Use the trig identity {{{cos(2theta) = cos^2(theta) - sin^2(theta)}}} and simplify:
{{{sin^2(theta)=(1/2)(1 - cos(2theta))}}}
{{{sin^2(theta)=(1/2)(1 - (cos^2(theta) - sin^2(theta)))}}}
{{{sin^2(theta)=(1/2)(1 - cos^2(theta) + sin^2(theta))}}}
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Since {{{sin^2(theta) + cos^2(theta) = 1}}}, {{{sin^2(theta) = 1 - cos^2(theta)}}}, so use this to substitute {{{1 - cos^2(theta)}}} for {{{sin^2(theta)}}} and simplify:
{{{sin^2(theta)=(1/2)(1 - cos^2(theta) + sin^2(theta))}}}
{{{sin^2(theta)=(1/2)(sin^2(theta) + sin^2(theta))}}}
{{{sin^2(theta)=(1/2)(2sin^2(theta))}}}
{{{sin^2(theta)=sin^2(theta)}}}
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Yay! Both sides of the equation are the same, so you have verified the identity!
Let me know if you need any further clarification. =)