Question

show that 1+cot square a/1+ cosec a =cosec a​

Answer 1

$\bigstar \underline{\underline{\mathfrak {To\ Prove:-}}}$

• $\sf 1+\frac{cot^2A}{1-cosecA} =cosec A$

$\bigstar \underline{\underline{\mathfrak {Proof:-}}}$

We need to know :

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❥ Cosec²A - 1 = Cot²A

❥ a² - b² =(a+b)(a-b)

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LHS :-  $\sf 1+\frac{cot^2A}{1+cosecA}$

$\\ :\implies \sf 1+\frac{cosec^2A-1}{cosecA+1} \\\\\\:\implies \sf 1+\frac{(cosecA+1)(cosecA-1)}{cosecA+1} \\\\\\:\implies \sf 1 + cosecA-1 \\\\\\:\implies \pink{\bold{\underline{Cosec\ A}}}$

Hence proved !

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Answer 2

Answer:

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