Prove that 1 - sinA - cos A - cosA-1- sinA - 2 secA

LHS= 1+sin A #160; cos A #160; +cos A #160; 1+sin A #160; = (1+sin A ) ^ 2 +cos ^ 2 A #160; (1+sin A )cos A #160; = 1+2s ...

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Sign of Trigonometric Ratios in Different Quadrants

Prove that 1...

Question

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

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

\frac{1 - cos A + sin A}{sin A + cos A - 1} = \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{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A

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