Embibe Experts Solutions for Chapter: Trigonometric Ratios, Functions and Identities, Exercise 2: EXERCISE-2

Set of values of $x$ in $\left(-\pi ,\pi \right)$ for which $\left|4\sin x-1\right|<\sqrt{5}$ is given by

Let  $m=\tan 3$ and  $n=\sec 6$, then which of the following statement(s) does/do not hold good ?

If  $\sqrt{\frac{1-\sin A}{1+\sin A}}+\frac{\sin A}{\cos A}=\frac{1}{\cos A}$, for all permissible values of $A$, then $A$ belong to -

If $\sec A=\frac{17}{8}$and $cosecB=\frac{5}{4}$ then $\sec (A+B)$ can have the value equal to

Which of the following when simplified reduces to unity?

It is known that $\sin \beta =\frac{4}{5}$ & $0<\beta <\pi$, then the value of $\frac{\sqrt{3}\sin \left(\alpha +\beta \right)-{\displaystyle \frac{2}{\cos \frac{\pi }{6}}}\cos \left(\alpha +\beta \right)}{\sin \alpha }$ is

In a triangle $ABC$, angle $A$ is greater than angle $B$. If the measures of angles $A$ and $B$ satisfy the equation $2\tan x-k\left(1+{\tan }^{2}x\right)=0$, where $k\in (0,1)$, then the measure of the angle $C$ is -

If  $\frac{\sin 3\theta }{\sin \theta }=\frac{11}{25}$ then $\tan \frac{\theta }{2}$ can have the value equal to -