Correct Answer - Option 4 :
\(\dfrac{31}{25}\)
Concept:
\(\rm \sin \theta = \frac{Perpendicular}{Hypotenuse}\)
\(\rm \cos \theta = \frac{Base}{Hypotenuse} \)
sin2 θ + cos2 θ = 1
Calculation:
7 sinθ + 24 cosθ = 25
Dividing by 25 on both the sides, we get
\(\rm \frac{7}{25}\)sinθ + \(\rm \frac{24}{25}\)cosθ = 1 ....(i)
We know that,
sin2 θ + cos2 θ = 1
sin θ.sin θ + cos θ.cos θ = 1 ....(ii)
On comparing equ (i) and (ii)
sin θ = \(\rm \frac{7}{25}\)
cos θ = \(\rm \frac{24}{25}\)
Now, (sinθ + cosθ)
= \(\rm \frac{7}{25}\)+ \(\rm \frac{24}{25}\)
= \(\rm \frac{31}{25}\)