Question

please help me solve the 2nd question!

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Answer 1

Note:

(1) sec²θ - tan²θ = 1 (or) sec²θ = 1 + tan²θ.

(2) cosec²θ - cot²θ = 1 (or) cosec²θ = 1 + cot²θ.

(3) cotθ = 1/tanθ.

Now,

Given : √sec²θ + cosec²θ

⇒ √(1 + tan²θ) + (1 + cot²θ)

⇒ √1 + tan²θ + 1 + cot²θ

⇒ √2 + tan²θ + cot²θ

⇒ √2 * tanθ * cotθ + tan²θ + cot²θ {From (3)}

⇒ √(tanθ + cotθ)²

⇒ tanθ + cotθ.

Hope it helps!