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Prove that cos^2 theta+cos^2 theta×cot^2 theta=cot^2 theta |
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Answer» cos2Ɵ + cos2Ɵ x cot2Ɵ = cot2ƟLHS=taking\xa0cos2Ɵ common we get cos2Ɵ (1+\xa0cot2Ɵ) = cos2Ɵ x cosec2Ɵ =\xa0cos2Ɵ x 1/ sin2Ɵ =\xa0cot2Ɵ = R.H.S COS^2 THETA + COS^2 THETA X COT^2 THETA = COS^2 THETA + COS^2 THETA X COS^2THETA /SIN^2THETA (COT^2 THETA =COS^2 THETA/SIN^2 THETA)THEN, (COS^2 THETA X SIN^2 THETA + COS^4 THETA )/SIN^2THETA =COS^2 THETA (SIN^2 THETA + COS^2 THETA)/SIN^2 THETA (TAKING COS^2 THETA Common) =COS^2 THETA (1)/SIN^2 THETA (BECAUSE COS^2 THETA + SIN^2 THETA = 1 ) = COT^2 THETA. Hence Proved |
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