Let $\theta$ be the angle between two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ then $\frac{\hat{A}\times \hat{B}}{\hat{A}\cdot \hat{B}}$ is equal to :

Q. If $\theta$ is the angle between vectors a and b, and $|a\times b|=|a\cdot b|,$ then $\theta$ is equal to

Q. Which of the following expression is equal to $\cos \theta$, where $\theta$ is angle between $\overrightarrow{A}\text{and}\overrightarrow{B}$?

Q. Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be non zero vectors such that $(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}=\frac{1}{3}\left|\begin{array}{c}\overrightarrow{b}\end{array}\right|\left|\begin{array}{c}\overrightarrow{c}\end{array}\right|\left|\begin{array}{c}\overrightarrow{a}\end{array}\right|$. If $\theta$ is the acute angle between the vectors $\overrightarrow{b}$ and $\overrightarrow{c}$ then $\sin \theta$ equals

Q. If $\tan \theta -\cot \theta =a,\sin \theta +\cos \theta =b$, then $(b^2-1{)}^2(a^2+4)$ is equal to
$(\theta \ne \frac{(2n+1)\pi }{2}and\theta n\pi n\in I)$

Q. If $\tan \theta =\frac{a}{b}$, then $\frac{\sin \theta }{{\cos }^8\theta }+\frac{\cos \theta }{{\sin }^8\theta }=$