tan A/1-cot A + cot A/1- tan A = 1+ secA cosecA
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Step 1
First, we can simplify the left-hand side of the equation by finding a common denominator: tan A/1-cot A + cot A/1- tan A = (tan A - cot A)/(1 - cot A)(1 - tan A) Show more…
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$$ \frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=\sec A \operatorname{cosec} A+1 $$
$$ \frac{1-\tan A}{1+\tan A}=\frac{\cot A-1}{\cot A+1} $$
$$ (1+\cot A-\operatorname{cosec} A)(1+\tan A+\sec A)=2 $$
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