If θ is an acute angle and 9 sinθ + 40 cosθ = 41 , find the value of  \(\frac{sinθ}{tanθ}\)  + cosθ.

\(\frac{80}{41}\)

In equation → 9 sinθ + 40 cosθ = 41

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

9 sinθ + 40 cosθ = 41

↓             ↓              ↓

P            B              H

Therefore,

\(\frac{sinθ}{tanθ}\)  + cosθ = \(\frac{sinθ}{\frac{sinθ}{cosθ}}\)  + cosθ

= cosθ + cosθ

= 2 cosθ

= 2 × \(\frac{40}{41}\)

= \(\frac{80}{41}\)