Question

Evaluate \(\frac {1+cos \, \theta }{sin \, \theta } \)(cosec θ – cot θ).

(a) cosec θ + cot θ

(b) cot^2 θ + tan^2 θ

(c) cot θ – tan θ

(d) cosec^2 θ – cot^2 θ

The question was asked in quiz.

My doubt stems from Trigonometric Identities in section Trigonometry of Mathematics – Class 10

Answer 1

Correct choice is (d) cosec^2 θ – cot^2 θ

To explain I would say: \(\frac {1+cos \, \theta }{sin \, \theta } \)(cosec θ – cot θ) = \(\frac {1}{sin \, \theta }+ \frac {cos \, \theta }{sin \, \theta } \)(cosec θ – cot θ)

= (cosec θ + cot θ)(cosec θ – cot θ)

= cosec^2 θ – cot^2 θ