\(\frac{cos θ [ ( 1 - cot θ) cot θ + cosec^2 θ]}{(1 - cos θ) cot θ (1 + cot θ) ( cosec θ + cot θ)}\) is equal to?
Answer & explanation
Correct answer: option 1
\(\frac{cos θ [ (cot θ - cot^2 θ + cosec^2 θ)}{( 1 - cos θ) cot θ (1 + cot θ) (cosec θ + cot θ)}\)
(cosec2 θ - cot2 θ = 1, Multiplying an dividing the equation with cosec θ)
= \(\frac{cosec θ × cos θ (1+ cot θ)}{cosec θ ( 1 - cos θ) cot θ ( 1 + cot θ) ( cosec θ + cot θ)}\)
= \(\frac{cosec θ cos θ}{(cosec θ - cot θ) cot θ( cosec θ + cot θ)}\)
As, (a+ b)(a - b) = a2 - b2, cosec2 θ - cot2 θ = 1
= \(\frac{1}{sin θ}\) × \(\frac{cos θ}{cot θ}\) = \(\frac{cot θ}{cot θ}\) = 1