Question
( (3 sin theta+5 cos theta)^{2}=5^{2} )
Squaring on both sides.
( (3 sin theta)^{2}+(5 cos theta)^{2}+2 times 3 sin theta 5 cos theta=25 )
( left[a+b=a^{2}+b^{2}+2 a bright] )
( 9 sin ^{2} theta+25 cos ^{2} theta+30 sin theta cos theta=25 )
( 9left(1-cos ^{2} thetaright)+25left(1-sin ^{2} thetaright)+30 sin theta cos theta=25 )
( left[sin ^{2} theta+cos ^{2} theta=1right] )
( 9-9 cos ^{2} theta+25-25 sin ^{2} theta+30 sin theta cos theta=25 )
( 9+25-left(9 cos ^{2} theta+25 sin ^{2} theta-30 sin theta cos thetaright)=25 )
( 34-left(9 cos ^{2} theta+25 sin ^{2} theta-30 sin theta cos thetaright)=25 )
( -left(25 sin ^{2} theta+9 cos ^{2} theta-30 sin theta cos thetaright)=25-34 )
( left(25 sin ^{2} theta+9 cos ^{2} theta-30 sin theta cos thetaright)=9 )
( (5 sin theta-3 cos theta)^{2}=9 )
( (5 sin theta-3 cos theta)=sqrt{9} )
( (5 sin theta-3 cos theta)=pm 3 )
( mathrm{L.H.S}=mathrm{R.H.S} )

59. If 3 sin 0 + 5 cos 0 = 5, prove that 5 sino - 3 cos 0 = + 3.
Solution
