Question

Prove that cota-cosa=/cota+cosa=coseca-1/coseca-1

Answer 1

Step-by-step explanation:

cota-cosa/cota+cosa

=(cosa/sina)-cosa/(cosa/sina)+cosa

=cosa-sinacosa/cosa+sinacosa

=1-sina/1+sina

=coseca-1/coseca+1

Answer 2

$\small\mathbb{QUESTION \to: }$

Prove that cotA-cosA/cotA+cosA=cosecA-1/cosecA-1

$\small\mathbb{SOLUTION \leadsto: A} \\ \\ \sf\ \frac{cotA - cosA}{cotA + cosA} \\ \\ \sf\ \implies \frac{ \frac{cosA}{sinA } - cos A}{{ \frac{cosA}{sinA } } + cosA}\\ \\ \sf\ \implies \frac{ \frac{cosA - sinAcosA}{ \cancel{sinA}} }{ \frac{cosA + sinAcosA}{ \cancel{sinA}}} \\ \\ \sf\ \implies \frac{cosA - sinAcosA}{cosA + sinAcosA} \\ \\ \sf\ \implies \frac{cosA(1 - sinA)}{cosA(1 + sinA)} \\ \\ \sf\ \implies \frac{1 - sinA}{1 + sinA} \\ \\ \sf\ \implies \frac{1 - \frac{1}{cosecA} }{1 + \frac{1}{cosecA} } \\ \\ \sf\ \implies \frac{ \frac{cosecA - 1}{ \cancel{cosecA}} }{ \frac{cosecA + 1}{ \cancel{cosecA} }} \\ \\ \sf\boxed{ \sf{\implies \frac{cosecA - 1}{cosecA + 1}} \: \: \: \: \ddot \smile}$