If θ is an acute angle and 5 sinθ + 12 cosθ = 13, find the value of  \(\frac{sinθ}{tanθ}\)  + cosθ.

\(\frac{24}{13}\)

In equation → 5 sinθ + 12 cosθ = 13

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

5 sinθ + 12 cosθ = 13

↓             ↓              ↓

P            B              H

Therefore,

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

= cosθ + cosθ

= 2 cosθ

= 2 × \(\frac{12}{13}\)

= \(\frac{24}{13}\)