Question #fd2da

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Answer 1 · 2018-02-14T23:01:54

See below.

#LHS#

Using identities:

#color(red)(bb(cos(A+B)=cosAcosB-sinAsinB)#

#color(red)bb(sin(A+B)=sinAcosB+cosAsinB)#

#cos3t=cos(t+2t)#

#cos(t+2t)=costcos2t-sintsin2t#

#cos(2t)=cos(t+t)#

#cost(costcost-sintsint)-sintsin2t#

#(cos^3t-costsin^2t)-sintsin2t#

#sin2t=sin(t+t)#

#(cos^3t-costsin^2t)-sint(sintcost+sintcost)#

#(cos^3t-costsin^2t)-(sin^2tcost+sin^2tcost)#

#(cos^3t-costsin^2t)-(2sin^2tcost)#

#color(blue)(cos^3t-3sin^2tcost)#

#LHS-=RHS#