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Answer 1 · 2017-03-01T17:41:24

see below

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