Question

Prove that sin(60°+A)*cos(30°+A)+cos(60°+A)*sin(30°+A)=cos(A+B)​

Answer 1

Answer:

Evaluate the following : (i) sin 60 cos 30 + sin 30 cos 60 We know that, sin 60 = 3/2 cos 30 = 3/2 sin 30 = 1/2 cos 60 = 1/2 Putting all values sin 60 cos 30 + sin 30 cos 60 = ( 3/2) ( 3/2)+(1/2) (1/2) = ( 3 3)/(2 2)+1/(2 2) = 3/4 + 1/4 = (3 + 1)/4 = 4/4 = 1 Hence, sin 60 cos 30 + sin 30 cos 60 = 1