Let the function $:(0, \pi) \rightarrow R$ be defined by
$f (\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \theta)^4$
Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in\left\{\lambda_1 \pi, \ldots, \lambda_{ T } \pi\right\}$, where $0<\lambda_1<\cdots<\lambda_r<1$. Then the value of $\lambda_1+\cdots+\lambda_r$ is. . . . .
$0.40$
$0.50$
$0.60$
$0.70$
Find the value of $\cos \left(-1710^{\circ}\right)$.
If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $
If $\sin x=-\frac{3}{5}$, where $\pi < x < \frac{3 \pi}{2}$ then $80\left(\tan ^2 x-\cos x\right)$ is equal to :
$\cos 15^\circ = $
Find the value of $\sin \frac{31 \pi}{3}$.