Embibe Experts Solutions for Exercise 7: Assignment

The value of $\frac{{\sin }^{6}u+{\cos }^{6}u-1}{{\sin }^{4}u+{\cos }^{4}u-1}$ (where ever defined) is equal to _______.

If $\frac{{\sin }^{4}x}{2}+\frac{{\cos }^{4}x}{3}=\frac{1}{5}$ then, the value of ${\cot }^{2}x$ is equal to

The value of $\frac{\tan \left(\ln 6\right)-\tan \left(\ln 2\right)-\tan \left(\ln 3\right)}{\tan \left(\ln 6\right)·\tan \left(\ln 2\right)·\tan \left(\ln 3\right)}$ is equal to ______.

If ${\sin }^3\theta \cos \left(3\theta \right)+{\cos }^3\theta \sin \left(3\theta \right)=\frac{3}{8}$ then, the value of $\sin \left(4\theta \right)$ is equal to ___.

If $\cos \left(\frac{\pi }{4}-x\right)\cos 2x+\sin x\sin 2x\sec x=\cos x\sin 2x\sec x+\cos \left(\frac{\pi }{4}+x\right)\cos 2x$ then, the greatest possible value of ${\cos }^{2}x+{\sec }^{2}x$ is equal to ______.

If $\sin {\theta }_1=\cos {\theta }_2,$ then sum of all possible single-digit integer values which the expression $\frac{1}{\pi }\left({\theta }_1\pm {\theta }_2-\frac{\pi }{2}\right)$ can attain is equal to _____.

The number of solutions of the equation $\tan x+\sec x=2\cos x$ lying in the interval $\left[0,2\pi \right]$ is equal to _____.

Let $f\left(\theta \right)=\sin \theta +2\sin 2\theta -\sin 3\theta -3$, then the number of solutions of $f\left(\theta \right)=0$ in $\theta \in \left(0,\pi \right)$ is ______.