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Question

If cos2π6+x-sin2π6-x=k cos 2x then k = _____________.

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Solution

Givencos2π6+x-sin2π6-x=K cos2xL.H.S. is cosπ6+x2-sinπ6-x2=cosπ6 cosx-sinπ6 sinx2-sinπ6 cosx-cosπ6 sinx2using identities:-cosa+b=cosa cosb-sina sinband sina-b=sina cosb-cosa sinb=32cosx-12sinx2-12cosx-32sinx2=34cos2x+14sin2x-32sinx cosx-14cos2x+34sin2x-32sinx cosx=34cos2x-14cos2x+14sin2x-34sin2x=12cos2x-12sin2x=12cos2x-sin2x=12cos2x=R.H.S. i.e. K cos2xK=12 value of K is 12.

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