Tigonometry Identities based Practice Question of 14 March 2022

Question of The Day14-03-2022

If xcosθ + ysinθ = 24 and xsinθ – ycosθ = 7, then find the value of (13.75x² + 13.75y²)/125.

Answer

Correct Answer : d ) 68.75

Explanation :

According to the question

xcosθ + ysinθ = 24 …..(1)

xsinθ – ycosθ = 7……..(2)

we know that

If xcosθ + ysinθ = a, and

xsinθ – ycosθ = b

then (x² + y²)(sin²θ + cos²θ) = a² + b²

comparing eq (1) and (2) with the formula

⇒(x² + y²)(sin²θ + cos²θ) = 24² + 7²

⇒ 576 + 49 = 625

⇒(x² + y²)(sin²θ + cos²θ) = 625

⇒(x² + y²) = 625

⇒ 68.75

Hence, (d) is the correct answer.

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