# CAT Practice : Trigonometry

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Max and Min value of the given expression

## Trigonometric Identities

Q.11: If $tan \phi + sin \phi = m , tan \phi - sin \phi = n ,$ Find the value of m2 = n2
1. 2√mn
2. 4√mn
3. m – n
4. 2mn

Choice B. 4√mn

## Detailed Solution

$tan \phi = \frac{(m+n)}{2}$
Subtracting the same,
$sin \phi = \frac{(m-n)}{2}$
Since, there are no available direct formula for relation between $sin \phi$ $tan \phi$ but we know that
$cosec^2 \phi – cos^2 \phi = 1$
$(\frac{2}{(m-n)})^2 - (\frac{2}{(m+n)})^2 = 1$
=)$\frac{(4((m+n)^2 - (m-n)^2))}{(m^2-n^2)^2} = 1$
=) $(m^2-n^2)^2 = 4(4mn)$
=) m2 - n2 = 4√mn

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