Question

Evaluate cosec θ sec θ.

(a) cos θ + tan θ

(b) cos θ – tan θ

(c) tan θ – cot θ

(d) cot θ + tan θ

I have been asked this question in final exam.

Asked question is from Trigonometric Identities in section Trigonometry of Mathematics – Class 10

Answer 1

Right choice is (d) cot θ + tan θ

The explanation: cosec θ sec θ = \(\frac {1}{sin \, \theta } \frac {1}{cos \, \theta } \)

= \(\frac {1}{sin \, \theta \, cos \, \theta } \)(cos^2θ + sin^2θ)

= \(\frac {cos \, \theta }{sin \, \theta } + \frac {sin \, \theta }{cos \, \theta } \)

= cot θ + tan θ