Question

\({(cos^3θ + sin^3θ) \over (cosθ + sinθ)} + {(cos^3θ – sin^3θ) \over (cosθ – sinθ)} = ?\)

Answer 1

Correct Answer - Option 3 : 2

Given:

We have to find the value of \({(cos^3θ + sin^3θ) \over (cosθ + sinθ)} + {(cos^3θ – sin^3θ) \over (cosθ – sinθ)}\)

Concept Used:

a³ + b³ = (a + b)(a² – ab + b²)

a³ – b³ = (a – b)(a² + ab + b²)

sin²θ + cos²θ = 1

Calculation:

\({(cos^3θ + sin^3θ) \over (cosθ + sinθ)} + {(cos^3θ – sin^3θ) \over (cosθ – sinθ)}\)

\(⇒ {(cosθ + sinθ)(cos^2θ - sinθ cosθ + sin^2θ) \over (cosθ + sinθ)} + {(cosθ – sinθ)(cos^2θ + cosθ sinθ + sin^2θ) \over (cosθ – sinθ)}\)

⇒ (cos²θ  – cosθsinθ + sin²θ) + (cos²θ + cosθsinθ + sin²θ)

⇒ 2(cos²θ + sin²θ)

⇒ 2