Q.5 (2) Taking θ = 30º to verify the following Trigonometric identities :(i) \(\sin^2\theta + \cos^2\theta = 1\)(ii) \(1 + \tan^2\theta = \sec^2\theta\)(iii) \(1 + \cot^2\theta = \operatorname{cosec}^2\theta\).

Doubtly Asked 24 Oct 2026 ssc 10th Save WhatsApp Report

1 answer

Best answer

Answer: All three identities hold for θ = 30º.

sin 30º = \(\tfrac12\), cos 30º = \(\tfrac{\sqrt3}{2}\), tan 30º = \(\tfrac{1}{\sqrt3}\), sec 30º = \(\tfrac{2}{\sqrt3}\), cot 30º = \(\sqrt3\), cosec 30º = 2.

(i) \(\tfrac14 + \tfrac34 = 1\) = RHS.

(ii) LHS = \(1 + \tfrac13 = \tfrac43\); RHS = \(\left(\tfrac{2}{\sqrt3}\right)^2 = \tfrac43\). LHS = RHS.

(iii) LHS = \(1 + 3 = 4\); RHS = \(2^2 = 4\). LHS = RHS.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?

Q.5 (2) Taking θ = 30º to verify the following Trigonometric identities :(i) \(\sin^2\theta + \cos^2\theta = 1\)(ii) \(1 + \tan^2\theta = \sec^2\theta\)(iii) \(1 + \cot^2\theta = \operatorname{cosec}^2\theta\).

1 answer

Your answer