Question

if tan theta=a/b, then find the value of 5 cos theta+4 sin theta/5 cos theta-4 sin theta

Answer 1

$tan \theta = \frac{a}{b} \\ given \\ \frac{ 5 \cos\theta + 4 \sin\theta}{5 \cos\theta - 4 \sin\theta} \\ divide \: with \: cos \theta \\ = \frac{5+ 4tan\theta}{5 - 4tan \theta} \\ = \frac{5 + 4\frac{a}{b} }{5 - 4\frac{a}{b} } \\ = \frac{5b + 4a}{5b - 4a}$

hope it helps.