Question

If 5tan$\theta$=4, then value of (5sin$\theta$ -4cos$\theta$)/(5sin$\theta$ +4cos$\theta$) is:

• A. $\frac{5}{3}$
• B. 0
• C. $\frac{5}{6}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B

0

Divide both numerator and denominator by cos $\theta$ and solve

$\frac{(5sin\theta -4cos\theta )}{(5sin\theta +4cos\theta )}$

= $\frac{\frac{(5sin\theta -4cos\theta )}{cos\theta }}{\frac{(5sin\theta +4cos\theta )}{cos\theta }}$

= $\frac{5tan\theta -4}{5tan\theta +4}$

= $\frac{4-4}{4+4}$
( since, given that 5 tan $\theta$ = 4 )

= 0