Question

If 5 tan A = 4, show that 5 sin A - 3 cos
A÷
5 cos A + 2 sin A=
1
6​

Answer 1

\frac{1}{6}

Step-by-step explanation:

Given that ,  

5 tan theta = 4  

tan theta = 4/5  

We know that  

tan theta = Sin theta/Cot theta  

 Say X  

Sin theta = 4x  

Cos theta = 5x  

Evaluate the values of LHS Side  

\frac{5 \ Sin\theta - 3\ Cos\theta}{5\ Sin\theta +  \ 2Cos\theta}

=> \frac{(5 * 4 )- (3 * 5) }{(5 * 4) + (2 * 5)}

=> \frac{20 -15}{20+ 10}

=> \frac{5}{30}

=> \frac{1}{6}

Hence Proved