If x/a cos theta+y/b sin theta=1 and x/a sin theta-y/b cos theta=1, prove that x square/a square+y square/b square=2

xacosθ+ybsinθ =1........(1)xasinθ-ybcosθ =1..........(2)Now squaring (1) and (2) we getx2a2cos2θ+y2b2sin2θ +2xyabcosθsinθ =1........(3)x2a2sin2θ+y2b2cos2θ -2xyabcosθsinθ =1.........(4)Now adding (3) and (4) we getx2a2(cos2θ+sin2θ)+y2b2(sin2θ +cos2θ)=2x2a2+y2b2=2          (cos2θ+sin2θ=1)

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