- 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
If \( 8 \tan A=15 \), find \( \sin A-\cos A \)
Given:
\( 8 \tan A=15 \).
To do:
We have to find \( \sin A-\cos A \).
Solution:
Let, in a triangle $ABC$ right-angled at $B$, $8\ tan\ A = 15$.
This implies,
$tan\ A=\frac{15}{8}$
We know that,
In a right-angled triangle $ABC$ with right angle at $B$,
By Pythagoras theorem,
$AC^2=AB^2+BC^2$
By trigonometric ratios definitions,
$sin\ A=\frac{Opposite}{Hypotenuse}=\frac{BC}{AC}$
$cos\ A=\frac{Adjacent}{Hypotenuse}=\frac{AB}{AC}$
$tan\ A=\frac{Opposite}{Adjacent}=\frac{BC}{AB}$
Here,
$AC^2=AB^2+BC^2$
$\Rightarrow AC^2=(8)^2+(15)^2$
$\Rightarrow AC^2=64+225$
$\Rightarrow AC=\sqrt{289}=17$
Therefore,
$sin\ A=\frac{BC}{AC}=\frac{15}{17}$
$cos\ A=\frac{AB}{AC}=\frac{8}{17}$
This implies,$\sin A-\cos A=\frac{15}{17}-\frac{8}{17}$
$=\frac{15-8}{17}$
$=\frac{7}{17}$
The value of $\sin A-\cos A$ is $\frac{7}{17}$.