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If x = a cosθ + b sinθ and y = a sinθ - b cosθ, then what is (x2 + y2) equal to?
- a)2ab
- b)a + b
- c)a2 + b2
- d)a2 - b2
Correct answer is option 'C'. Can you explain this answer?
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If x = a cosθ + b sinθ and y = a sinθ - b cosθ...
Given x = a cosθ + b sinθ and y = a sinθ - b cosθ;
(x2 + y2) = (a cosθ + b sinθ)2 + (a sinθ - b cosθ)2
⇒ a2cos2θ + b2sin2θ + 2sinθ cosθ + a2cos2θ + b2sin2θ - 2sinθ cosθ
⇒ a2(cos2θ + sin2θ) + b2(cos2θ + sin2θ)
⇒ a2 + b2
⇒ a2 + b2
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If x = a cosθ + b sinθ and y = a sinθ - b cosθ...
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If x = a cosθ + b sinθ and y = a sinθ - b cosθ...
Given x = a cosθ + b sinθ and y = a sinθ - b cosθ;
(x2 + y2) = (a cosθ + b sinθ)2 + (a sinθ - b cosθ)2
⇒ a2cos2θ + b2sin2θ + 2sinθ cosθ + a2cos2θ + b2sin2θ - 2sinθ cosθ
⇒ a2(cos2θ + sin2θ) + b2(cos2θ + sin2θ)
⇒ a2 + b2
⇒ a2 + b2
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If x = a cosθ + b sinθ and y = a sinθ - b cosθ, then what is (x2+ y2) equal to?a)2abb)a + bc)a2+ b2d)a2- b2Correct answer is option 'C'. Can you explain this answer?
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