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 × \(\frac{15}{17}\)

= \(\frac{30}{17}\)