Q.1 (ii) The value of sin[sin⁻¹(-1/√(2)) - 3sin⁻¹(√(3)/2)] = A. -1/√(2) B. 1/√(2) C. √(3)/2 D. -√(3)/2

Answer: B. 1/√(2) Answer: (b) 1/√(2) sin⁻¹(-1/√(2)) = -π/4 and sin⁻¹(√(3)/2) = π/3 , so 3sin⁻¹(√(3)/2) = π . sin(-π/4 - π) = -sin(π + π/4) = -(-sinπ/4) = 1/√(2) .

The value of \(\sin\left[\sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) - 3\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)\right] =\)

Q.1 (ii) The value of \(\sin\left[\sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) - 3\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)\right] =\)

A. \(-\frac{1}{\sqrt{2}}\)

B. \(\frac{1}{\sqrt{2}}\)

C. \(\frac{\sqrt{3}}{2}\)

D. \(-\frac{\sqrt{3}}{2}\)

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

1 answer

Best answer

Answer: B. \(\frac{1}{\sqrt{2}}\)

Answer: (b) \(\frac{1}{\sqrt{2}}\)

\(\sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) = -\frac{\pi}{4}\) and \(\sin^{-1}\left(\frac{\sqrt{3}}{2}\right) = \frac{\pi}{3}\), so \(3\sin^{-1}\left(\frac{\sqrt{3}}{2}\right) = \pi\).

\(\sin\left(-\frac{\pi}{4} - \pi\right) = -\sin\left(\pi + \frac{\pi}{4}\right) = -\left(-\sin\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?

The value of \(\sin\left[\sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) - 3\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)\right] =\)

1 answer

Your answer