已知xcosθ=a,y/tanθ=b(a≠0,b≠0),求证x^2/a^2-y^2/b^2=1

cosθ=a/xsinθ/cosθ=tanθ=y/b所以sinθ=cosθ*y/b=ay/(bx)sin²θ+cos²θ=1所以 a²/x²+a²y²/b²x²=1两边乘x²a²+a²y²/b²=x²1+y²/b²=x²/a²所以x²/a²-y²/b²=1