How do you verify #costheta(1-4sin^2theta)=costhetacos(2theta)-sinthetasin(2theta)#?

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Answer 1 · 2016-11-21T19:09:14

see below

#cos theta(1-4sin^2 theta)=cos theta cos2 theta-sin theta sin 2 theta#

Use the formulas : #cos 2 theta=1-2sin^2 theta, sin 2theta=2sinthetacos theta#

Right Side : #=cos theta cos2 theta-sin theta sin 2 theta#

#=cos theta (1-2sin^2theta)-sin theta*2sin theta cos theta#

#=cos theta (1-2sin^2theta-2sin^2theta)#

#=cos theta(1-4sin^2 theta)#

#:.=# Left Side