Prove that A-cosA A- cos A -A-1 A-1

cot A cos A/cot A + cos A= cosec A 1/cosec +1 on solving LHS are get cos A/sin A cos A/cos A/sin A+cos A=cos (1/sin A 1)/cos A (1/sin A)+1[∵1/sin A= ...

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Standard XII

Mathematics

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

Prove that ...

Question

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

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Solution

$\frac{c o t A - c o s A}{c o t A + c o s A} = \frac{c o s e c A - 1}{c o s e c + 1}$
on solving LHS are get
$\frac{\frac{c o s A}{s i n A} - c o s A}{\frac{c o s A}{s i n A} + c o s A} = \frac{c o s (\frac{1}{s i n A} - 1)}{c o s A (\frac{1}{s i n A}) + 1} [∵ \frac{1}{s i n A} = c o s e c A]$
$\frac{c o s e c A - 1}{c o s e c A + 1} = R H S$

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Prove that cotA−cosAcotA+cosA=cscA−1cscA+1

cotA−cosAcotA+cosA=cosecA−1cosec+1on solving LHS are getcosAsinA−cosAcosAsinA+cosA=cos(1sinA−1)cosA(1sinA)+1[∵1sinA=cosecA]cosecA−1cosecA+1=RHS

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