Question #7facb

1 Answer
Mar 1, 2017

see below

Explanation:

I think you meant to write pi/4 instead of pi4. So here it is with pi/4

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

sqrt2 cos(pi/4+theta)=sqrt2[cos (pi/4) cos theta-sin(pi/4) sin theta]

=sqrt2[1/sqrt2 cos theta-1/sqrt2 sin theta]

=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