![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:
$ \frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1 $
Given:
\( \frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1 \)
To do:
We have to evaluate \( \frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1 \).
Solution:
We know that,
$cot\ (90^{\circ}- \theta) = tan\ \theta$
Therefore,
$\frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1=\frac{\tan 35^{\circ}}{\cot (90^{\circ}-35^{\circ})}+\frac{\cot (90^{\circ}-12^{\circ})}{\tan 12^{\circ}}-1$
$=\frac{\tan 35^{\circ}}{\tan 35^{\circ}}+\frac{\tan 12^{\circ}}{\tan 12^{\circ}}-1$
$=1+1-1$
$=1$
Therefore, $\frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1=1$.
Advertisements