If θ is an acute angle and 9 sinθ + 40 cosθ = 41 , find the value of \(\frac{sinθ}{tanθ}\) + cosθ.
Answer & explanation
Correct answer: option 1
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 × \(\frac{40}{41}\)
= \(\frac{80}{41}\)