The set of all real values of $\lambda $ for which the function $f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$has exactly one maxima and exactly one minima, is :

Question

The set of all real values of $\lambda $ for which the function

$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$

has exactly one maxima and exactly one minima, is :

$\left( { - {3 \over 2},{3 \over 2}} \right) - \left\{ 0 \right\}$

$\left( { - {3 \over 2},{3 \over 2}} \right)$

$\left( { - {1 \over 2},{1 \over 2}} \right) - \left\{ 0 \right\}$

$\left( { - {1 \over 2},{1 \over 2}} \right)$

Solution

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