![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 the following trigonometric identities:
\( \left(\sec ^{2} \theta-1\right)\left(\operatorname{cosec}^{2} \theta-1\right)=1 \)
To do:
We have to prove that \( \left(\sec ^{2} \theta-1\right)\left(\operatorname{cosec}^{2} \theta-1\right)=1 \).
Solution: We know that,
$\sec ^{2} A-tan ^{2} A=1$.......(i)
$\operatorname{cosec}^{2} A-cot ^{2} A=1$.......(ii)
$ \tan ^2 A\times\cot ^2 A=1$.......(iii)
Therefore,
$\left(\sec ^{2} \theta-1\right)\left(\operatorname{cosec}^{2} \theta-1\right)=(\tan ^{2} \theta)(\cot ^{2} \theta)$ (From (i) and (ii))
$=\tan ^{2} \theta \times \cot ^{2} \theta$
$=1$ (From (iii))
Hence proved.
Advertisements