Question

If 5 cos θ – 12 sin θ = 0, find the value of (sinθ+cosθ)/(2cosθ-sinθ).​

Answer 1

Answer:

5cosx = 12sinx

or, sinx/cosx =5/12

or, tanx = 5/12

secx = 13/12

cosx= 12/13

sinx = 5/13

cosx+sinx = 17/13

2cosx-sinx= 19/13

thus your answer is 17/19

Answer 2

Answer:

$</p><p>5cosθ−12sinθ=0</p><p></p><p></p><p></p><p>$

$⇒5cosθ=12sinθ</p><p></p><p>$

$⇒cotθ= \frac{12}{5}$

$\frac{sinθ + cosθ}{2cosθ - sinθ} = \frac{sinθ(1 + cotθ)}{sinθ(2cotθ - 1)}$

$= \frac{1 + \frac{12}{5} }{2 \times \frac{12}{5} - 1}$

$= \frac{ \frac{17}{5} }{ \frac{24}{5} - 1 }$

$= \frac{ \frac{17}{5} }{ \frac{24 - 5}{5} }$

$= \frac{17}{5} \times \frac{5}{19}$

$= \frac{17}{19}$