Question #7facb

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Question #7facb

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Answer 1 · 2017-03-01T17:41:24

see below

Explanation:

I think you meant to write $\frac{π}{4}$ $pi/4$ instead of $π 4$ $pi4$ . So here it is with $\frac{π}{4}$ $pi/4$

Right Hand Side:
Use the formula $cos (A + B) = cos A cos B - sin A sin B$ $cos(A+B)=cosAcosB-sinAsinB$

$\sqrt{2} cos (\frac{π}{4} + θ) = \sqrt{2} [cos (\frac{π}{4}) cos θ - sin (\frac{π}{4}) sin θ]$ $sqrt2 cos(pi/4+theta)=sqrt2[cos (pi/4) cos theta-sin(pi/4) sin theta]$

$= \sqrt{2} [\frac{1}{\sqrt{2}} cos θ - \frac{1}{\sqrt{2}} sin θ]$ $=sqrt2[1/sqrt2 cos theta-1/sqrt2 sin theta]$

$= \frac{\sqrt{2}}{\sqrt{2}} cos θ - \frac{\sqrt{2}}{\sqrt{2}} sin θ$ $=sqrt2/sqrt2 cos theta-sqrt2/sqrt2 sin theta$

$=cancel(sqrt2/sqrt2) cos theta-cancel(sqrt2/sqrt2) sin theta$

$=cos theta-sin theta$

$:.=$ Left Hand Side

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Question #7facb

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