- Trending Categories
- 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 : $( sin \theta+ cosec \theta)^{2}+( cos \theta+sec \theta)^{2} =7+ tan^{2} \theta+ cot^{2} \theta$.
Given: $( sin \theta+ cosec \theta)^{2}+( cos \theta+sec \theta)^{2} =7+ tan^{2} \theta+ cot^{2} \theta$.
To do: To prove $L.H.S.=R.H.S.$
Solution:
$L.H.S.=(sin \theta+ cosec \theta)^{2}+(cos \theta+sec \theta)^{2}$
$=sin^{2} \theta+cosec^{2} \theta+2sin \theta cosec \theta+cos^{2} \theta+sec^{2} \theta+2cos \theta sec \theta$
$=sin^{2} \theta+cos^{2} \theta+2sin \theta cosec \theta+sec^{2} \theta+cosec^{2} \theta+2cos \theta sec \theta$
$=1+2+2+sec^{2} \theta+cosec^{2} \theta$ [$\because sin^{2}\theta + cos^{2}\theta=1$, $sin \theta=\frac{1}{cosec \theta}$ and $cos \theta=\frac{1}{sec \theta}$]
$=5+1+tan^{2} \theta+1+cot^{2} \theta$ [$sec^{2} \theta=1+tan^{2} \theta$ and $cosec^{2} \theta=1+cot^{2} \theta$]
$=7+tan^{2} \theta+cot^{2} \theta$
$=R.H.S.$
Hence proved that $L.H.S.=R.H.S.$
Advertisements