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DERRAN
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Homework Statement
Prove that sin(45+x).sin(45-x) = [tex]\frac{1}{2}[/tex]cos2x
Homework Equations
double angle formulae
reduction formulae
special angles
identities
The Attempt at a Solution
(sin45.cosx+cos45.sinx)(sin45.cosx-cos45.sinx)
=(sin45.cosx-cos45.sinx)2
=([tex]\frac{1}{\sqrt{2}}[/tex]cosx-[tex]\frac{1}{\sqrt{2}}[/tex]sinx)2
=[tex]\frac{1}{2}[/tex]cos2x-sinx.cosx+[tex]\frac{1}{2}[/tex]sinx2
=[tex]\frac{1}{2}[/tex]-sinx.cosx