If x - cot A - cos A and y - cot A - cos A- prove that x-y-x-y2 - x-y-22 - 1-

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Trigonometric Identities

If x = cot A ...

Question

If x = cot A + cos A and y = cot A - cos A, prove that

$(\frac{x - y}{x + y})^{2} + (\frac{x - y}{2})^{2} = 1$ .

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x = (cot A + cos A) and y = (cot A - cos A)

{(\frac{x - y}{x + y})}^{2} + {(\frac{x - y}{2})}^{2} = 1

If x = cosec A + cos A and y = cosec A - cos A then prove that

$(\frac{2}{x + y})^{2} + (\frac{x - y}{2})^{2} - 1 = 0$

x = cosec A + cos A

y = cosec A - cos A

{(\frac{2}{x + y})}^{2} + {(\frac{x - y}{2})}^{2} - 1 = 0

sin A + sin 2 A = x, cos A = x, cos A + cos 2 A = y,

(x^{2} + y^{2}) (x^{2} + y^{2} - 3) = 2 y

\sqrt{\frac{1 + cos A}{1 - cos A}} = \frac{x}{y}

tan A =

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