If a = xcosθ + ysinθ and b = xsinθ - ycosθ, then a2 + b2 is equal to:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. x2 + y2.
Given, a = xcosθ + ysinθ
And b = xsinθ - ycosθ
Squarying both equations and adding them,
⇒ a2 + b2 = (xcosθ + ysinθ)2 + (xsinθ - ycosθ)2
⇒ a2 + b2 = x2cos2θ + y2sin2θ + 2xysinθcosθ + x2sin2θ + y2cos2θ - 2xysinθcosθ
⇒ a2 + b2 = x2(sin2θ + cos2θ) + y2(sin2θ + cos2θ)
⇒ a2 + b2 = x2 + y2