How do you verify the identity $cos((5pi)/4-x)=-sqrt2/2(cosx+sinx)$ ?

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Answer 1 · 2017-02-06T08:53:17

Please see below.

We will use the identities $cos(pi+theta)=-costheta$ and $cos(A-B)=cosAcosB+sinAsinB$

Hence, $cos((5pi)/4-x)$

= $cos(pi+(pi/4-x))$

= $-cos(pi/4-x)$

= $-[cos(pi/4)cosx+sin(pi/4)sinx]$

= $-[sqrt2/2cosx+sqrt2/2sinx]$

= $-sqrt2/2(cosx+sinx)$

How do you verify the identity cos((5pi)/4-x)=-sqrt2/2(cosx+sinx)cos((5pi)/4-x)=-sqrt2/2(cosx+sinx)?