The value of $\frac{\cot \left(54°\right)}{\tan \left(36°\right)} + \frac{\tan \left(20°\right)}{\cot \left(70°\right)}$ is

• 0

• 2

• 3

• 1

If $\sin \left(6\mathrm{\theta }\right) + \sin \left(4\mathrm{\theta }\right) + \sin \left(2\mathrm{\theta }\right) = 0$, then the general value of $\mathrm{\theta }$

• $\frac{\mathrm{n\pi }}{4}, \mathrm{n\pi } \pm \frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{n\pi }}{4}, \mathrm{n\pi } \pm \frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{n\pi }}{4}, 2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{n\pi }}{4}, 2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{6}$

In a $∆\mathrm{ABC}$, 2ac$\sin \left(\frac{\mathrm{A} - \mathrm{B} +\hspace{0.17em}\mathrm{C}}{2}\right)$ is equal to

• a² + b² - c²

• c² + a² - b²

• b² - a² - c²

• c² - a² - b²

Value of ${\tan }^{-1}\left(\frac{\sin \left(2\right) - 1}{\cos \left(2\right)}\right)$

• $\frac{\mathrm{\pi }}{2} - 1$

• $1 - \frac{\mathrm{\pi }}{4}$

• $2 - \frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4} - 1$

The value of $\frac{\sin \left(55°\right) - \cos \left(55°\right)}{\sin \left(10°\right)}$ is

• $\frac{1}{\sqrt{2}}$

• 2

• 1

• $\sqrt{2}$

In triangle ABC, a = 2, b = 3 and sin(A) = $\frac{2}{3}$, then B is equal to

• 30$°$

• 60$°$

• 90$°$

• 120$°$

77.

Simplest form of $\frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos \left(4\mathrm{x}\right)}}}}$ is

• $\sec \left(\frac{\mathrm{x}}{2}\right)$

• $\sec \left(\mathrm{x}\right)$

• $\csc \left(\mathrm{x}\right)$

• 1

If $5\cos \left(2\mathrm{\theta }\right) + 2{\cos }^2\left(\frac{\mathrm{\theta }}{2}\right) + 1 = 0$, when $\left(0 < \mathrm{\theta } < \mathrm{\pi }\right)$, then the values of $\mathrm{\theta }$ are

• $\frac{\mathrm{\pi }}{3} \pm \mathrm{\pi }$

• $\frac{\mathrm{\pi }}{3}, {\cos }^{-1}\left(\frac{3}{5}\right)$

• ${\cos }^{-1}\left(\frac{3}{5}\right) \pm \mathrm{\pi }$

• $\frac{\mathrm{\pi }}{3}, \mathrm{\pi } - {\cos }^{-1}\left(\frac{3}{5}\right)$

$\tan \left[\frac{\mathrm{\pi }}{4} + \frac{1}{2}{\cos }^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right] + \tan \left[\frac{\mathrm{\pi }}{4} - \frac{1}{2}{\cos }^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right]$ is equal to

• $\frac{2\mathrm{a}}{\mathrm{b}}$

• $\frac{2\mathrm{b}}{\mathrm{a}}$

• $\frac{\mathrm{a}}{\mathrm{b}}$

• $\frac{\mathrm{b}}{\mathrm{a}}$

The equation $\sqrt{3}\sin \left(\mathrm{x}\right) + \cos \left(\mathrm{x}\right)$ = 4 has

• only one solution

• two solutions

• infinitely many solutions

• no solution