The value of $2(\sin^6 \theta + \cos^6 \theta) - 3(\sin^4 \theta + \cos^4 \theta) + 1$ is

If $\frac{\sec 8\theta - 1}{\sec 4\theta - 1} = \frac{a + b\tan^2 2\theta}{1 + c\tan^2 2\theta + d\tan^4 2\theta}$ (where $\theta \neq \frac{n\pi}{16}, n \in I$),then the value of $(a - b + c - d)$ is -

If $x = r \cos \theta \cos \phi$,$y = r \cos \theta \sin \phi$,and $z = r \sin \theta$,then the value of $x^{2} + y^{2} + z^{2}$ is

The expression $\frac{\tan^2 20^\circ - \sin^2 20^\circ}{\tan^2 20^\circ \cdot \sin^2 20^\circ}$ simplifies to

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to

If $x \sin^{2} 60^{\circ} - \frac{3}{2} \sec 60^{\circ} \tan^{2} 30^{\circ} + \frac{4}{5} \sin^{2} 45^{\circ} \tan^{2} 60^{\circ} = 0$,then $x$ is