Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 1871

If \(4 \sin ^{-1} x+3 \cos ^{-1} x=2 \pi\), then \(x=\) (a) 1 (b) \(-1\) (c) \((1 / 2)\) (d) \(-(1 / 2)\)

Short Answer

Expert verified
\(x=1\) (Option (a)).

Step by step solution

01

Test option (a) - 1

Plug in \(x=1\) into the given equation: \[4 \sin ^{-1}(1) + 3 \cos ^{-1}(1) = 2 \pi\] We know that \(\sin^{-1}(1)=\frac{\pi}{2}\) and \(\cos^{-1}(1)=0\). So the equation becomes: \[4 \left(\frac{\pi}{2}\right) + 3 (0) = 2 \pi\] Simplifying this equation gives: \[2\pi = 2\pi\] The equation holds true, so the answer is: \(x=1\) (Option (a)).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The number of solution of the equation \(\sqrt{(3) \sin x+\cos x}=4\) is \(x \in[0,2 \pi]\) (a) 1 (b) 2 (c) 0 (d) 3

If \(\tan (x / 2)=\operatorname{cosec} x-\sin x\) then \(\tan ^{2}(x / 2)=\) (a) \(\sqrt{5}+1\) (b) \(\sqrt{5}-1\) (c) \(\sqrt{5}-2\) (d) \(\sqrt{5}+2\)

If \(3 \cos x+4 \sin x=K\) has a possible solution then number of values of integral \(\mathrm{K}\) is (a) 3 (b) 5 (c) 10 (d) 11

\(15 \sin ^{4} x+10 \cos ^{4} x=6\) then \(\tan ^{2} x=\) (a) \((2 / 5)\) (b) \((1 / 3)\) (c) \((3 / 5)\) (d) \((2 / 3)\)

If \(\sin A=3 \sin (A+2 B)\) angle \(B\) is acute and \(A\) is obtuse: then (a) \(\tan \mathrm{B}=(1 / \sqrt{2})\) (b) \(\tan B>(1 / \sqrt{2})\) (c) \(\tan \mathrm{B}<(1 / \sqrt{2})\) (d) \(0<\tan B<(1 / \sqrt{2})\)
See all solutions

Recommended explanations on English Textbooks

Summary Text

Read Explanation

Essay Plan

Read Explanation

Rhetorical Analysis Essay

Read Explanation

Single Paragraph Essay

Read Explanation

Prosody

Read Explanation

Discourse

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free