Question

If A =30°. Show that i) 4Cosa Cos (60° - A) = Cos 3A
ii) Sin3A = 3SinA - 4 Sin A​

Answer 1

Answer:

sin(2a+a)

=sin2a.cosa+cos2a.sina

=2sina.cosa.cosa+(cos^2 a-sin^2a)sina

=2sina.cos^2 a+sina-2sin^3a

=2sina(1-sin^2a)+sina-2sin^3 a

=2sina-2sin^3a+sina-2sin^3a

=3sin-4sin^3 a

= cos (2A) cos (A) - sin(2A) sin(A)

= [ 2cos^2(A) - 1 ] cos (A) - (2 sin A cos A )sin A

= 2cos^3(A) - cos A - 2sin^2(A) cos A

= 2cos^3(A) - cos A - 2( 1 - cos^2(A)) cos A

= 2cos^3(A) - cos A - 2cos A + 2cos^3(A)

= 4cos^3(A) - 3cos A=RHS.