Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The number of solutions of the equation <img alt="32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}" src="https://entrancecorner.codecogs.com/gif.latex?32%5E%7B%5Ctan%20%5E%7B2%7D%20x%7D&plus;32%5E%7B%5Csec%20%5E%7B2%7D%20x%7D%3D81%2C0%

The number of solutions of the equation 32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4} is :
Option: 1 0
Option: 2 2
Option: 3 1
Option: 4 3

Answers (1)

best_answer

32^{\tan^{2}x}+32^{1+\tan^{2}x}= 81\\

32^{\tan^{2}x}=t\\

\Rightarrow t+32t=81\\

\Rightarrow 33t=81\Rightarrow t=\frac{81}{33}\\

\Rightarrow 32^{\tan^{2}x}=\frac{81}{33}=\frac{27}{11}\\

\Rightarrow \tan^{2}x=\log_{32}\frac{27}{11}\in\left ( 0,1 \right )\\

\Rightarrow x=\tan^{-1}\sqrt{\log_{32}\frac{27}{11}}For \; 0\leq x\leq \pi/4\\

\Rightarrow only\; 1 \; solution

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 registration ends tomorrow; changes introduced in exam this year
anam-khan

BTech Admission 2025 Live: JEE Mains registrations closing tomorrow; VITEEE, MET exam dates out
anam-khan

JEE Main 2025 Live: NTA to close JEE registration on Friday; apply at jeemain.nta.nic.in, correction window

Latest Question