Question

Prove that (cos^3θ+sin^3θ)/(cosθ+sinθ)+(cos^3θ-sin^3θ)/(cosθ-sinθ)=2.

Answer 1

Hey mate

Here is ur answer

$( {cos}^{3} + \: {sin}^{3}) \div (cos + sin) + \\ ({cos}^{3} - {sin}^{3} ) \div (cos - sin) = 2 \\ lhs = ( {cos}^{3} + {sin}^{3} ) \div (cos + sin) \\ + ({cos}^{3} - {sin}^{3} ) \div (cos - sin) \\ ({cos}^{2} + {sin}^{2} )(cos+ sin) \div (cos + sin) \\ ( {cos}^{2} + {sin}^{2} )(cos - sin) \div (cos - sin) \\ ( {cos}^{2} + {sin}^{2} ) + ( {cos}^{2} + {sin}^{2} ) \\ { \: identity \: = {cos}^{2} + {sin}^{2} = 1} \\ 1 + 1 \\ 2 \\ lhs = rhs \\ hence \: proved$