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You know the experation for the area of a circle of radius R. It is Pi*R2.
But what about the formula for the area of an ellipse of semi-minor axis of length A and semi-major axis of length B? (These semi-major axes are half the lengths of, respectively, the smallest and largest diameters of the ellipse)
For example, the following is a standard formula for such an ellipse centered at the origin:
(x2/A2) + (y2/B2) = 1.
The area of such an ellipse is
Area = Pi * A * B ,
a very natural generalization of the formula for a circle!
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1/cos(x-a)cos(x-b)
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If tanA+sinA=m and tanA-sinA=n, show that m 2 -n 2 = 4√mn Ans: TanA + SinA = m TanA - SinA = n. m 2 -n 2 =4√mn . m 2 -n 2 = (TanA + SinA) 2 -(TanA - SinA) 2
1 1/3:2/3:1/6
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