Q.1 (i) cos[tan⁻¹(1/3)+tan⁻¹(1/2)]= ____. A. sqrt3/2 B. 1/2 C. 1/sqrt2 D. π/4

Answer: C. 1/sqrt2 Answer: (c) 1/sqrt2 tan⁻¹1/3+tan⁻¹1/2=tan⁻¹(1/3+1/2/1-1/3·1/2)=tan⁻¹(5/6/5/6)=tan⁻¹1=π/4 . So the value is cosπ/4=1/sqrt2 .

Chapter: Trigonometric Functions· Mathematics & Statistics Part 1

\(\cos\left[\tan^{-1}\left(\dfrac{1}{3}\right)+\tan^{-1}\left(\dfrac{1}{2}\right)\right]=\) ____.

Q.1 (i) \(\cos\left[\tan^{-1}\left(\dfrac{1}{3}\right)+\tan^{-1}\left(\dfrac{1}{2}\right)\right]=\) ____.

A. \(\dfrac{\sqrt3}{2}\)

B. \(\dfrac12\)

C. \(\dfrac{1}{\sqrt2}\)

D. \(\dfrac{\pi}{4}\)

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: C. \(\dfrac{1}{\sqrt2}\)

Answer: (c) \(\dfrac{1}{\sqrt2}\)

\(\tan^{-1}\dfrac13+\tan^{-1}\dfrac12=\tan^{-1}\left(\dfrac{\frac13+\frac12}{1-\frac13\cdot\frac12}\right)=\tan^{-1}\left(\dfrac{5/6}{5/6}\right)=\tan^{-1}1=\dfrac{\pi}{4}\).

So the value is \(\cos\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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\(\cos\left[\tan^{-1}\left(\dfrac{1}{3}\right)+\tan^{-1}\left(\dfrac{1}{2}\right)\right]=\) ____.

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