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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