Prove the following trigonometric identities- cot-A-cos-A-cot-A-cos-A-cosec-A-1-cosec-A-1

LHS = cot A cos A/cot A+cos A = cosA/sinA cosA/cosA/sinA + cosA = cosecAcosA cosA/cosecAcosA + cosA = cosA(cosecA 1)/cosA(cosecA +1) = cosecA 1/cosecA + ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

Prove the fol...

Question

Prove the following trigonometric identities:

$\frac{c o t A - c o s A}{c o t A + c o s A} = \frac{c o s e c A - 1}{c o s e c A + 1}$

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Solution

$L H S = \frac{c o t A - c o s A}{c o t A + c o s A}$

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

$= \frac{c o s e c A c o s A - c o s A}{c o s e c A c o s A + c o s A}$

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

$= \frac{c o s e c A - 1}{c o s e c A + 1}$

$= R H S$

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Prove the following trigonometric identities: cot A−cos Acot A+cos A=cosec A−1cosec A+1

LHS=cot A−cos Acot A+cos A =cosAsinA−cosAcosAsinA+cosA =cosecAcosA−cosAcosecAcosA+cosA =cosA(cosecA−1)cosA(cosecA+1) =cosecA−1cosecA+1 =RHS

Prove the following trigonometric identities:

$\frac{c o t A - c o s A}{c o t A + c o s A} = \frac{c o s e c A - 1}{c o s e c A + 1}$