Question

prove cot a - 1 + cosec a /cota+1 -cosec a= cot a + cosec a​

Answer 1

$\huge\mathbb\red{Answer:-}$

cotA−cosA

  sinAcosA+cosAsinAcosA−cosA=cosA+cosAsinAcosA−cosAsinA

                             =cosA(1+sinA)cosA(1−sinA)

                        =sinA1+sinAsinAsinA1−cosAsinA   

                             =cosecA+1cosecA−1

Answer 2

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

$\displaystyle \: \frac{CotA - 1 + CosecA}{CotA + 1 - CosecA}$

$= \displaystyle \: \frac{CotA + CosecA - 1}{CotA - CosecA + 1}$

$= \displaystyle \: \frac{CotA + CosecA - ( {Cosec}^{2}A - {Cot}^{2}A) }{CotA + 1 - CosecA}$

$=\frac{(CotA + CosecA )-(CosecA + CotA )(CosecA - CotA ) }{CotA + 1 - CosecA}$

$= \frac{(CotA + CosecA )(CotA + 1 - CosecA)}{(CotA + 1 - CosecA)}$

$= (CotA + CosecA)$