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 - Maths - Introduction to Trigonometry

Question

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

Utsav · Accepted Answer

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)=2⇒x2a2+y2b2=2 (∵cos2θ+sin2θ=1)