Question

1+cot^2alpha/1+cosec^2 alpha=cosec

Answer 1

Answer:

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

Step-by-step explanation:

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

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

\*By algebraic identity:

cot²A = cosec²A-1 */

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

/* By algebraic identity:

a²-b² = (a+b)(a-b) */

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

After cancellation, we get

$=1+ cosec\alpha - 1$

$= cosec\alpha$

$= RHS$

Therefore,

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

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Answer 2

Answer:

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