Prove that cosA1-sinA-1-sinAcosA-2secA

cos A1+sin A=cos A (1 sin A)1 sin^2 A=cos A(1 sin A)cos^2 A=1 sin Acos A LHS=cos A1+sin A+1+sin Acos A=1 sin A+1+sin Acos A=2secA ...

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Trigonometric Ratios

Prove that ...

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Prove that $\frac{c o s A}{1 + s i n A} + \frac{1 + s i n A}{c o s A} = 2 s e c A$

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

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

Prove the identity cos2A/1+sinA+1+sinA/cosA=2secA

\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{2}{2 s i n^{2} A - 1} = \frac{2}{1 - 2 c o s^{2} A}

\frac{1 + c o s A}{s i n A} + \frac{s i n A}{1 + c o s A} = 2 c o s e c A

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