If θ is an acute angle and 8 sinθ + 15 cosθ = 17 , find the value of  $\frac{sinθ}{tanθ}$  + cosθ.

$\frac{30}{17}$

In equation → 8 sinθ + 15 cosθ = 17

If the coefficients of sinθ and cosθ and constant are making a triplet then →

8 sinθ + 15 cosθ = 17

↓             ↓              ↓

P            B              H

Therefore,

$\frac{sinθ}{tanθ}$  + cosθ = $\frac{sinθ}{\frac{sinθ}{cosθ}}$  + cosθ

= cosθ + cosθ

= 2 cosθ

= 2 × $\frac{15}{17}$

= $\frac{30}{17}$