How do you prove sin3θ = 3cos^2θ sinθ -sin^3θ ?

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Answer 1 · 2018-08-12T16:31:39

Please see below.

We have to prove :

#sin3θ = 3cos^2θ sinθ -sin^3θ #

We know that ,

#color(brown)((1)sin(x+y)=sinxcosy+cosxsiny#

Let ,

#LHS=sin3theta#

#LHS=sin(2theta+theta)to[use, (1)]#

#LHS=color(red)(sin2theta)costheta+color(blue)(cos2theta)sintheta#

#LHS=color(red)(2sinthetacostheta)costheta+color(blue)((cos^2theta-sin^2theta))sintheta#

#LHS=2cos^2thetasintheta+cos^2thetasintheta-sin^3theta#

#LHS=3cos^2thetasintheta-sin^3theta#

#LHS=RHS#