![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
Evaluate the following:
$ \tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} $
Given:
\( \tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} \)
To do:
We have to evaluate \( \tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} \).
Solution:
We know that,
$tan\ (90^{\circ}- \theta) = cot\ \theta$
$tan\ \theta \times \cot\ \theta=1$
Therefore,
$\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ}=\tan (90^{\circ}-42^{\circ})\tan 23^{\circ}\tan 42^{\circ}\tan (90^{\circ}-23^{\circ})$
$=\tan 42^{\circ}\tan 23^{\circ}\cot 42^{\circ}\cot 23^{\circ}$
$=(\tan 42^{\circ}\cot 42^{\circ})(\tan 23^{\circ}\cot 23^{\circ})$
$=1\times1$
$=1$
Therefore, $\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ}=1$.
Advertisements