यदि 7 sinθ + 24 cosθ = 25 तो (sin θ + cos θ) का मूल्य क्या है?

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This question was previously asked in

NDA (Held On: 18 Apr 2021) Maths Previous Year paper

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Answer 1

अवधारणा:

\(\rm \sin \theta = \frac{Perpendicular}{Hypotenuse}\)

\(\rm \cos \theta = \frac{Base}{Hypotenuse} \)

sin2 θ + cos2 θ = 1

गणना:

7 sinθ + 24 cosθ = 25

दोनों तरफ से 25 को विभाजित करके, हम प्राप्त करते हैं

\(\rm \frac{7}{25}\)sinθ + \(\rm \frac{24}{25}\)cosθ = 1 ....(i)

हम जानते हैं कि,

sin²θ + cos²θ = 1

sin θ.sin θ + cos θ.cos θ = 1 ....(ii)

समीकरण (i) और (ii) तुलना करने पर

sin θ = \(\rm \frac{7}{25}\)

cos θ = \(\rm \frac{24}{25}\)

अब, (sinθ + cosθ)

= \(\rm \frac{7}{25}\)+ \(\rm \frac{24}{25}\)

= \(\rm \frac{31}{25}\)