Question

If sinθ =cotθ , then the value of cos^2 θ + 2cos^3 θ + cos^4 θ is
(A) 2 (B) 3 (C) 1 (D) 0 (E) none of the above

Answer 1

given: sinθ =cotθ
sinθ = cosθ/sinθ
cosθ = sin^2 θ
cosθ = 1 - cos^2 θ
cos^2 θ = 1 - cosθ

then cos^2 θ + 2cos^3 θ + cos^4 θ
= cos^2 θ(1 + 2cosθ + cos^2 θ)
= (1 - cosθ)(1 + 2cosθ + 1 - cosθ)
= (1 - cosθ)(2 + cosθ)
= 2 - cosθ - cos^2 θ
= 2 - cosθ - (1 - cosθ)
= 1

Answer 2

thank u!