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Maths-

General

Easy

Question

If cot $theta equals fraction numerator square root of m plus square root of n over denominator square root of m minus square root of n end root end fraction$ ,then $left parenthesis m plus n right parenthesis$ cos $2 theta$ is equal to

$2 \sqrt{m n}$
$\frac{m + n}{m - n}$
$(\sqrt{m} + \sqrt{n})^{2}$
$None of these$

The correct answer is: $2 square root of m n end root$

Given $theta equals fraction numerator square root of m minus square root of n over denominator square root of m plus square root of n end root end fraction$ . so
$cos invisible function application 2 theta equals fraction numerator 1 minus tan to the power of 2 end exponent invisible function application theta over denominator 1 plus tan to the power of 2 end exponent invisible function application theta end fraction equals fraction numerator 1 minus open parentheses fraction numerator square root of m minus square root of n over denominator square root of m plus square root of n end fraction close parentheses to the power of 2 end exponent over denominator 1 plus open parentheses fraction numerator square root of m minus square root of n over denominator square root of m plus square root of n end fraction close parentheses to the power of 2 end exponent end fraction$
$equals fraction numerator 4 square root of m n end root over denominator 2 left parenthesis m plus n right parenthesis end fraction$
$rightwards double arrow open parentheses m plus n close parentheses cos invisible function application 2 theta equals 2 square root of m n end root$

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