Question

prove that 1+cot^2alpha/1+cosce alpha=cosec alpha

Answer 1

Answer:

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Answer 2

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Prove that $\sf 1 + \frac{ { \cot}^{2} \alpha }{1 + \cosec \alpha } = \cosec \alpha$

$\star\:\:\:\sf\large\underline\blue{Proof:-}$

Taking LHS,

$\sf 1 + \frac{ { \cot }^{2} \alpha }{ 1 + \cosec \alpha }$

$= \sf 1 + \frac{ { \cosec^{2} \alpha - 1 }}{ 1 + \cosec \alpha }$

$= \sf 1 + \frac{ {( \cosec \alpha - 1 ) \cancel{( \cosec \alpha + 1)} }}{ \cancel{( 1 + \cosec \alpha) } }$

$\sf = 1 + \cosec \alpha - 1$

$= \sf \cosec \alpha$

Taking RHS,

$= \sf \cosec \alpha$

Therefore,

$\boxed{ \sf 1 + \frac{ { \cot}^{2} \alpha }{1 + \cosec \alpha } = \cosec \alpha }$

Hence Proved.