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\(\frac{cos^3θ+sin^3θ}{cosθ+sinθ}\) + \(\frac{cos^3θ-sin^3θ}{cosθ-sinθ}\) = 2 |
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Answer» LHS = \(\cfrac{cos^3θ+sin^3θ}{cosθ+sinθ}\) + \(\cfrac{cos^3θ-sin^3θ}{cosθ-sinθ}\) = \(\cfrac{(cosθ+sinθ)(cos^2θ-cosθsinθ+sin^2θ)}{cosθ+sinθ}\) + \(\cfrac{(cosθ-sinθ)(cos^2θ+cosθsinθ+sin^2θ)}{cosθ-sinθ}\) = (cos2 θ + sin2 θ − cos θ sin θ) + (cos2 θ + sin2 θ + cos θ sin θ) = (1 − cos θ sin θ) + (1 + cos θ sin θ) = 2 = RHS Hence, LHS = RHS |
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