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