![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the value of \( x \) in each of the following:
\( \sqrt{3} \tan 2 x=\cos 60^{\circ}+\sin 45^{\circ} \cos 45^{\circ} \)
Given:
\( \sqrt{3} \tan 2 x=\cos 60^{\circ}+\sin 45^{\circ} \cos 45^{\circ} \)
To do:
We have to find the value of \( x \).
Solution:
\( \sqrt{3} \tan 2 x=\cos 60^{\circ}+\sin 45^{\circ} \cos 45^{\circ} \)
We know that,
$\cos 60^{\circ}=\frac{1}{2}$
$\sin 45^{\circ}=\frac{1}{\sqrt2}$
$\cos 45^{\circ}=\frac{1}{\sqrt2}$
\( \sqrt{3} \tan 2 x=\cos 60^{\circ}+\sin 45^{\circ} \cos 45^{\circ} \)
$\Rightarrow \sqrt{3} \tan 2 x=\frac{1}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt2}$
$\Rightarrow \sqrt{3} \tan 2 x=\frac{1}{2}+\frac{1}{2}$
$\Rightarrow \sqrt{3} \tan 2 x=1$
$\Rightarrow \tan 2 x=\frac{1}{\sqrt3}$
$\Rightarrow \tan 2 x=\tan 30^{\circ}$ (Since $\tan 30^{\circ}=\frac{1}{\sqrt3}$)
Comparing on both sides, we get,
$2x=30^{\circ}$
$x=\frac{30^{\circ}}{2}$
$x=15^{\circ}$
Hence, the value of $x$ is $15^{\circ}$.