If $\sin x+\sin ^2 x=1, x \in\left(0, \frac{\pi}{2}\right)$, then $\left(\cos ^{12} x+\tan ^{12} x\right)+3\left(\cos ^{10} x+\tan ^{10} x+\cos ^8 x+\tan ^8 x\right)$ $+\left(\cos ^6 x+\tan ^6 x\right)$ is equal to

  • [JEE MAIN 2025]
  • A
    $4$
  • B
    $3$
  • C
    $2$
  • D
    $1$

Similar Questions

Prove that

$3 \sin \frac{\pi}{6} \sec \frac{\pi}{3}-4 \sin \frac{5 \pi}{6} \cot \frac{\pi}{4}=1$

If $\left| {\cos \,\theta \,\left\{ {\sin \theta + \sqrt {{{\sin }^2}\theta + {{\sin }^2}\alpha } } \right\}\,} \right|\, \le k,$ then the value of $k$ is

If $\sin \theta = \frac{{24}}{{25}}$ and $\theta $ lies in the second quadrant, then $\sec \theta + \tan \theta = $

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

If $\sin \theta + {\rm{cosec}}\theta = 2,$ the value of ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ is