Prove that sin(x)^2 - 5cos(x)^2 = 6sin(x)^2 - 5
5 = 5(cos(x)^2 + sin(x)^2) = 5cos(x)^2 + 5sin(x)^2=> 5 - 5cos(x)^2 = 5sin(x)^2=> sin(x)^2 + 5 - 5cos(x)^2 = 6sin(x)^2=> sin(x)^2 - 5cos(x)^2 = 6sin(x)^2 - 5
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l1 and l2 are tangents of a circle. l1 intersects the circle at (3-√3,5) with a gradient of √3, and l2 intersects the circle at (3+√2,4+√2) with a gradient of -1. Find the centre of the circle, and hence find the radius of the circle.
