The value of \(\frac{cos^3 θ + sin^3 θ}{cos θ + sin θ}\) + \(\frac{cos^3 θ - sin^3 θ}{cos θ - sin θ}\) is?
Answer & explanation
Correct answer: option 3
\(\frac{cos^3 θ + sin^3 θ}{cos θ + sin θ}\) + \(\frac{cos^3 θ - sin^3 θ}{cos θ - sin θ}\)
= \(\frac{(cos θ + sin θ) (cos^2 θ + sin^2 θ - sin θ cos θ)}{(cos θ + sin θ)}\) + \(\frac{(cos θ - sin θ) (cos^2 θ + sin^2 θ + sin θ cos θ)}{(cos θ - sin θ)}\)
(because a3 + b3 = (a + b)(a2 + b2 - ab) and a3 - b3 = (a - b)(a2 + b2 + ab))
= cos2 θ + sin2 θ - sin θ cos θ + cos2 θ + sin2 θ + sin θ cos θ
= 1 + 1 = 2
(because, cos2 θ + sin2 θ = 1)