Question

PROVE THAT :
1 +(cos^2A/1+cosecA) =cosec A​

Answer 1

1 +(cot^2A/1+cosecA)

=(1+cosecA+cot^2A)/(1+cosecA)

we know (cosec^A-cot^2A=1)

=(cosec^2A+cosecA)/(1+cosecA)

=(cosecA)(cosecA+1)/(1+cosecA)

=cosecA

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Answer 2

$1 + \frac{ {cot}^{2} a}{1 + coseca} \\ \\ = \frac{1 + coseca + {cot}^{2} a}{1 + coseca} \\ \\ = \frac{ {cosec}^{2}a + coseca }{1 + coseca} \\ \\ = \frac{coseca(1 + coseca)}{1 + coseca } \\ \\ = coseca$