If θ is an acute angle and 24 sinθ + 7 cosθ = 25 , find the value of \(\frac{sinθ}{tanθ}\) + cosθ.
Answer & explanation
Correct answer: option 2
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 × \(\frac{7}{25}\)
= \(\frac{14}{25}\)