Embibe Experts Solutions for Chapter: Trigonometric Ratios and Identities, Exercise 1: JKCET 2019

If $5\sin x=3,$ then what is the value of $\left\{\frac{(\sec x-\tan x)}{(\sec x+\tan x)+5}\right\}$?

If $W, X, Y$ and $Z$ are four angles taken in order of a cyclic quadrilateral, then the value of $(13+\cot W+\cot X+\cot Y+\cot Z+13)$ is

If  $f\left(x\right)=\sqrt{\left[\right(\sin 2x+2\left)\right(\cos 2x+2\left)\right]}$ for $x$ is a real number, then which of the following values lies in the domain of $f\left(x\right)$ but NOT in the range of $f\left(x\right) ?$

If $cosec39°=q,$ then the value of $\frac{1}{{cosec}^2{51}^{°}}+{\sin }^2{39}^{°}+{\tan }^2{51}^{°}-\frac{1}{{\sin }^2{51}^{°}{\sec }^2{39}^{°}}+1$ is

In a triangle $PQR, A, B$ and $C$ are the angles opposite to the corresponding sides of lengths $a, b$ and $c$, respectively. If the sides are $a=5, b=13$ and $c=12$, then $\sin \frac{B}{2}+\cos \frac{B}{2}=$

If $\alpha +\beta =\frac{\mathrm{\pi }}{2}$ and $\beta +\gamma =\alpha$, then $\sin \gamma =$

The sum of the series: $\mathrm{sinp}+x\sin \left(p+q\right)+\frac{x^2}{2!}\sin (p+2\mathrm{q})+\cdots \infty$ is

If $S={\sin }^{2}p-\frac{1}{2}\sin \left(2\mathrm{p}\right)\left({\sin }^{2}p\right)+\frac{1}{3}\sin \left(3\mathrm{p}\right)\left({\sin }^{3}p\right)-\frac{1}{4}\sin \left(4\mathrm{p}\right)\left(\left({\sin }^{4}p\right)+\cdots \infty \right.$ then $\tan S=$