![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
Prove that:$ \frac{\sin 70^{\circ}}{\cos 20^{\circ}}+\frac{\operatorname{cosec} 20^{\circ}}{\sec 70^{\circ}}-2 \cos 70^{\circ} \operatorname{cosec} 20^{\circ}=0 $
To do:
We have to prove that $\frac{\sin 70^{\circ}}{\cos 20^{\circ}}+\frac{\operatorname{cosec} 20^{\circ}}{\sec 70^{\circ}}-2 \cos 70^{\circ} \operatorname{cosec} 20^{\circ}=0$.
Solution:
We know that,
$sin\ (90^{\circ}- \theta) = cos\ \theta$
$sec\ (90^{\circ}- \theta) = \operatorname{cosec}\ \theta$
$cos\ (90^{\circ}- \theta) = sin\ \theta$
$sin\ \theta \times \operatorname{cosec}\ \theta=1$
Therefore,
$\frac{\sin 70^{\circ}}{\cos 20^{\circ}}+\frac{\operatorname{cosec} 20^{\circ}}{\sec 70^{\circ}}-2 \cos 70^{\circ} \operatorname{cosec} 20^{\circ}=\frac{\sin (90^{\circ}- 20^{\circ})}{\cos 20^{\circ}}+\frac{\operatorname{cosec} 20^{\circ}}{\sec (90^{\circ}- 20^{\circ})}-2 \cos (90^{\circ}- 20^{\circ}) \operatorname{cosec} 20^{\circ}$
$=\frac{\cos 20^{\circ}}{\cos 20^{\circ}}+\frac{\operatorname{cosec} 20^{\circ}}{\operatorname{cosec} 20^{\circ}}-2 \sin 20^{\circ} \operatorname{cosec} 20^{\circ}$
$=1+1-2(1)$
$=2-2$
$=0$
Hence proved.