If cosɵ - sinɵ = x and If sinɵ + cosɵ = y, then show that x2 + y2 =2 please dont spam
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Answered by
14
Answer:
a cosθ - b sinθ = x and a sinθ + b cosθ = y
R.H.S. = x2 + y2
= (a cosθ - b sinθ)2 + (a sinθ + b cosθ)2
= a2cos2θ - 2ab cosθ sinθ + b2sin2θ + a2sin2θ + 2absinθ cosθ + b2cos2θ
= (a2+b2) cos2θ + (b2+a2)sin2θ
= (a2+b2)cos2θ + (a2+b2)sin2θ
= (a2+b2)(cos2θ + sin2θ)
= (a2+b2) [∵ cos2θ + sin2θ = 1]
= L.H.S. ∴ a2+b2 = x2+y2.
Explanation:
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Answered by
9
Answer:
a cosθ - b sinθ = x and a sinθ + b cosθ = y
R.H.S. = x2 + y2
= (a cosθ - b sinθ)2 + (a sinθ + b cosθ)2
= a2cos2θ - 2ab cosθ sinθ + b2sin2θ + a2sin2θ + 2absinθ cosθ + b2cos2θ
= (a2+b2) cos2θ + (b2+a2)sin2θ
= (a2+b2)cos2θ + (a2+b2)sin2θ
= (a2+b2)(cos2θ + sin2θ)
= (a2+b2) [∵ cos2θ + sin2θ = 1]
= L.H.S. ∴ a2+b2 = x2+y2.
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