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Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Prove that A...

Question

Prove that
$\frac{cot A - cos A}{cot A + cos A} = \frac{cos e c A - 1}{cos e c A + 1}$

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Solution

$\Rightarrow \frac{c o t A - c o s A}{c o t A + c o s A} = \frac{c o s e c A - 1}{c o s e c A + 1}$
$\Rightarrow \frac{\frac{c o s A}{s i n A} - c o s A}{\frac{c o s A}{s i n A} + c o s A} = \frac{c o s A (\frac{1}{s i n A} - 1)}{c o s A (\frac{1}{s i n A} + 1)}$
$\Rightarrow \frac{c o s e c A - 1}{c o s e c + 1}$

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Q. Prove the following trigonometric identities.

\frac{\cot A - \cos A}{\cot A + \cos A} = \frac{cosec A - 1}{cosec A + 1}

\frac{\cot A - \cos A}{\cot A + \cos A} = \frac{cosec A - 1}{cosec A + 1}

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

\frac{cos A cot A - sin A tan A}{c o s e c A - sec A} = 1 + sin A cos A

\frac{cot A - cos A}{cot A + cos A} = \frac{cos e c A - 1}{cos e c A + 1}

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Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Standard XII Mathematics

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