Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$-\lambda ={\sin }^4\theta +{\cos }^4\theta$

$={\left({\sin }^2\theta +{\cos }^2\theta \right)}^2-2{\sin }^2\theta {\cos }^2\theta$

$=1-\frac{4{\sin }^2\theta {\cos }^2\theta }{2}$

$=1-\frac{{\sin }^{2}2\theta }{2}$

$\Rightarrow \lambda =\frac{{\sin }^{2}2\theta }{2}-1$

$\lambda \in \left[-1,-\frac{1}{2}\right]$