Question #a8634

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Answer 1 · 2016-12-18T14:06:25

#LHS=(cos ^3 theta - cos3 theta)/costheta + (sin^3theta + sin3theta)/sintheta#

#=(cos ^3 theta - 4cos^3 theta+3costheta)/cos theta + (sin ^3 theta + 3sintheta-4sin^3theta)/sin theta #

#=(3costheta - 3cos^3 theta)/cos theta + (3sintheta -3sin^3theta)/sin theta #

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

#=6 - 3(cos^2 theta +sin^2theta)#

#=6-3*1=3=RHS#

Proved