get app

Go To Your Study Dashboard

The number of solutions of the equation $1+\sin ^{4}x=\cos ^{2}3x,$ $x\equiv \left [ -\frac{5\pi }{2},\frac{5\pi }{2} \right ]$ is :

Option 1)
$4$

Option 2)
$3$

Option 3)
$5$

Option 4)
$7$

Answers (1)

V Vakul

Trigonometric Identities -

$\sin ^{2}\Theta + \cos ^{2}\Theta = 1$

$1 + \tan ^{2}\Theta = \sec ^{2}\Theta$

$1 + \cot ^{2}\Theta = cosec ^{2}\Theta$

- wherein

They are true for all real values of $\Theta$

Results from General Solution -

$\sin \Theta = 0 \Rightarrow \Theta = n\pi$

-

$1+\sin ^{4}x=\cos ^{2}3x$ $x\equiv \left [ \frac{-5\pi }{2},\frac{5\pi }{2} \right ]$

Rewrite the trignometric equation

$1-\cos ^{2}\left ( 3x \right )+\sin ^{4}x=0$

$\because \sin ^{2}\left ( x \right )+\cos ^{2}\left ( x \right )=1$

$\sin ^{2}\left ( 3x \right )+\sin ^{4}\left ( x \right )=0$

$\Rightarrow \sin \left ( 3x \right )=0\: \: \: \: \: \: and\: \: \: \: \sin \left ( x \right )=0$

$\sin \left ( x \right )=0$ at $x=0,\pi ,-\pi,-2\pi,2\pi$

This value is also true for $\sin \left ( 3x \right )$

Option 1)

$4$

Option 2)

$3$

Option 3)

$5$

Option 4)

$7$

Similar Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 6999/-

Buy Now

Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 14999/-

Buy Now

Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 4999/-

Buy Now

Knockout JEE Main April 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-

Buy Now

JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 9999/-

Buy Now

Boost your Preparation for JEE Main 2021 with Personlized Coaching

Start Now

Exams

Articles

Questions