If θ is an acute angle and 24 sinθ + 7 cosθ = 25 , find the value of  \(\frac{sinθ}{tanθ}\)  + cosθ.

 \(\frac{14}{25}\)

In equation → 24 sinθ + 7 cosθ = 25

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

24 sinθ + 7 cosθ = 25

↓             ↓              ↓

P            B              H

Therefore,

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

= cosθ + cosθ

= 2 cosθ

= 2 × \(\frac{7}{25}\)

= \(\frac{14}{25}\)