Question

1 + cot^2A÷1 + cosecA=cosecA

Answer 1

Step-by-step explanation:

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Given,.

1 + cot²A÷1 + cosecA=cosecA

=>>> L.H.S

=(1+cosecA + cot²A)/1+cosecA

=(1+cosecA + cosec²A - 1)/(1+cosecA)

=(cosecA + cosec²A)/(1+cosecA)

=[cosecA (1+cosecA)]/(1+cosecA)

=cosecA

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Answer 2

Correct Question :-

$\bf\:prove:1+\dfrac{cot^{2}A}{1+cosecA}=cosecA$

Solution :-

Taking LHS , we get,

$\sf\:1+\dfrac{cot^{2}A}{1+cosecA} \\ \\ \bf \: taking \: lcm\\\\\sf \frac{1+cosecA+cot^{2}A}{1+cosecA}\\\\\sf\frac{cosecA+(1+cot^{2}A)}{1+cosecA}\\\\\bf\:putting\: (1+cot^{2}A)=cosec^{2}A\\\\ \sf\frac{cosecA+cosec^{2}A}{1+cosecA} \\ \\ \bf \: taking \:cosecA \:common\:from\:numerator \\ \\ \sf\frac{cosecA\cancel{(1+cosecA)}}{\cancel{(1+cosecA)}} \\ \\ \large\boxed{\bf \: cosecA}=\bf\: RHS(Proved)$