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. . . . . 

  • [IIT 2020]
  • A

    $0.40$

  • B

    $0.50$

  • C

    $0.60$

  • D

    $0.70$

Similar Questions

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 :

  • [JEE MAIN 2024]

$\cos 15^\circ = $

Find the value of $\sin \frac{31 \pi}{3}$.