Question

If xcosθ – ysinθ = a, xsinθ + ycos θ = b, prove that x²+y²=a²+b².

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Answer 1

Answer:

Answer

xcosθ−ysinθ=a..1)

xsinθ+ycosθ=b.2)

(1)

2

+(2)

2

(xcosθ−ysinθ)

2

+(xsinθ+ycosθ)

2

=a

2

+b

2

x

2

cos

2

θ+y

2

sin2θ−2xysinθcosθ+x

2

sin

2

θ+y

2

cos

2

θ+2xycosθsinθ=a

2

+b

2

x

2

(cos

2

θ+sin

2

θ)+y

2

(sin

2

θ+cos

2

θ)=a

2

+b

2

x

2

+y

2

=a

2

+b

2

Answer 2

Answer:

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