Range of Trigonometric Expressions

The number of integral values of $k$ for which the equation $\mathrm{}\mathrm{}\mathrm{}7\cos x+\mathrm{}\mathrm{}\mathrm{}5\sin x=\mathrm{}\mathrm{}\mathrm{}2k+1$ has a solution, is

If $A={\sin }^2\theta +{\cos }^4\theta ,$ then for all values of $\theta ,$ A lies in the interval

The minimum value of $3\cos x+4\sin x+18$ is :

Cotyledons are also called-

If ${\cos }^{4}x+{\sin }^{4}x-\sin 2x+\frac{3}{4}{\sin }^{2}2x=y$

If $\sin x+\mathrm{cosec}x+\tan y+\cot y=4,$ where $x\in \left(0,\frac{\pi }{2}\right]$ and $y\in \left(0,\frac{\pi }{2}\right),$ then $\tan \frac{y}{2}$ is a root of the equation

If $7\cos x-24\sin x=d\cos \left(x+\alpha \right), 0<\alpha <\frac{\pi }{2}.$ be true for all $x\in R,$ than

The greatest absolute integral value of $k$ for which the statement $7\cos x+5\sin x=2k+1$ is valid

$\sqrt{3}\sin x+\cos x$ is maximum, when $x$ is

The all values of expression $\left(5\cos \theta +3\cos \left(\theta +\frac{\pi }{3}\right)+3\right)$ lies between

If $A={\sin }^2\theta +{\cos }^4\theta ,$ then for all real values of $\theta$

The maximum value of $\left(4{\sin }^{2}x+3{\cos }^{2}x+\sin \frac{x}{2}+\cos \frac{x}{2}\right)$ is

The maximum value of $2\sin x+4\cos x+3$is

The range of the function $f\left(x\right)=\left[\mathrm{s}\mathrm{i}\mathrm{n}x+\mathrm{c}\mathrm{o}\mathrm{s}x\right]$ (where $\left[.\right]$ denotes the greatest integer function) is

The maximum value of  $\cos \left(\cos \left(\cos \left(\sin x\right)\right)\right)$ for all $x\in R$ is

The maximum value of 4 ${\sin }^{2}x+3{\cos }^{2}x+\sin \frac{x}{2}+\cos \frac{x}{2}$is

If$y=1+4{\sin }^{2}x{\cos }^{2}x,$ then

The maximum value of$\mathrm{ }\sin \left(x+\frac{\pi }{6}\right)+\cos \left(x+\frac{\pi }{6}\right)\mathrm{ }$in the interval $\left(0,\frac{\pi }{2}\right)$ is attained at

If$\sin \mathrm{\theta }+\cos \mathrm{\theta }=x,\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n} {\sin }^6\mathrm{\theta }+{\cos }^6\mathrm{\theta }=\frac{1}{4}\left[4-3{\left(x^2-1\right)}^2\right]$ for

The maximum value of ${\cos }^2\left(\frac{\pi }{3}-x\right)-{\cos }^2\left(\frac{\pi }{3}+x\right)$is