Question

cosec²θ + sec²θ is equal to ______.

विकल्प

• tan²θ + cot²θ

• cot θ + tan θ

• (cot θ + tan θ)²

• 1

Answer 1

cosec²θ + sec²θ is equal to (cot θ + tan θ)².

Explanation:

Use 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ.

So, cosec²θ + sec²θ = (1 + tan²θ) + (1 + cot²θ)

= tan²θ + cot²θ + 2 

= (tan θ + cot θ)²