(cosec θ − sin θ ) (sec θ − cos θ ) (tan θ + cot θ ) is equal

Question

Philoid · Accepted Answer

To find: (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ)

∵

∴ (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ)

Now, as sin² θ + cos ² θ = 1

⇒ sin² θ = 1 – cos² θ

And cos² θ = 1 – sin² θ

⇒ (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ)