6. prove that: 1+sin2A/cos2A=cosA+sinA/cosA-sinA

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\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{s i n^{2} A - c o s^{2} A}

\frac{1 + sin 2 A}{cos 2 A} = \frac{cos A + sin A}{cos A - sin A} = cot (\frac{π}{4} - A)

\frac{1 + cos A + sin A}{1 + cos A - sin A} = \frac{1 + sinA}{cos A}

\frac{sin 2 A}{sin A} - \frac{cos 2 A}{cos A} = sec A

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

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