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Maths-

General

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Question

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

$m^{2} - n^{2} = 4 m n$
$m^{2} + n^{2} = 4 m n$
$m^{2} - n^{2} = m^{2} + n^{2}$
$m^{2} - n^{2} = 4 \sqrt{m n}$

The correct answer is: $m to the power of 2 end exponent minus n to the power of 2 end exponent equals 4 square root of m n end root$

From the given relations , $m plus n equals 2 tan invisible function application theta comma blank m minus n equals 2 sin invisible function application theta$
$rightwards double arrow m to the power of 2 end exponent minus n to the power of 2 end exponent equals 4 tan invisible function application theta sin invisible function application theta$
Also $blank 4 square root of m n end root equals 4 square root of tan to the power of 2 end exponent invisible function application theta minus sin to the power of 2 end exponent invisible function application theta end root equals 4 sin invisible function application theta tan invisible function application theta$
$therefore$ From Eqs. (i) and (ii), we get $m to the power of 2 end exponent minus n to the power of 2 end exponent equals 4 square root of m n end root$

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