Trigonometric Ratios of Allied Angles

If  $\alpha +\beta +\gamma =\mathrm{}\mathrm{}\mathrm{}2\pi ,\mathrm{then}$ –

$\frac{{\sin }^2{\displaystyle \frac{\mathrm{\pi }}{18}}{\displaystyle +}{\displaystyle {\sin }^2}{\displaystyle \frac{{\displaystyle \mathrm{\pi }}}{{\displaystyle 9}}}{\displaystyle +}{\displaystyle {\sin }^2}{\displaystyle \frac{{\displaystyle 7\mathrm{\pi }}}{{\displaystyle 18}}}{\displaystyle +}{\displaystyle {\sin }^2}{\displaystyle \frac{{\displaystyle 4\mathrm{\pi }}}{{\displaystyle 18}}}}{{\cos }^2\frac{\mathrm{\pi }}{18}+{\cos }^2\frac{{\displaystyle \mathrm{\pi }}}{{\displaystyle 9}}+{\cos }^2\frac{{\displaystyle 7\mathrm{\pi }}}{{\displaystyle 18}}+{\cos }^2\frac{{\displaystyle 4\mathrm{\pi }}}{{\displaystyle 18}}}=$

$a^2\cos \left(\frac{2\mathrm{\pi }}{3}\right)-4a^2\tan \left(\frac{3\mathrm{\pi }}{4}\right)+2a^2{\sin }^2\left(\frac{2\mathrm{\pi }}{3}\right)=$

The value of $\frac{\tan 245°+\tan 335°}{\tan 205°-\tan 115°}$ is

The value of $\tan \left(\frac{7\pi }{8}\right)$ is

Find the value of $\frac{\sin \left(-{212}^{\circ }\right)\cos \left({302}^{\circ }\right)+{\cos }^2\left(-{148}^{\circ }\right)}{\sin \left(-{82}^{\circ }\right)\cos \left(-8^{\circ }\right)+\sin \left({368}^{\circ }\right)\sin \left(-{172}^{\circ }\right)}$

FInd the value of $\frac{\sin \left(-{212}^{\circ }\right)\cos {302}^{\circ }+{\cos }^2\left(-{148}^{\circ }\right)}{\sin \left(-{82}^{\circ }\right)\cos \left(-8^{\circ }\right)+\sin \left({368}^{\circ }\right)\sin \left(-{172}^{\circ }\right)}$

FInd the value of ${\sin }^2\left(3\mathrm{\pi }\right)+{\cos }^2\left(4\mathrm{\pi }\right)+{\tan }^2\left(5\mathrm{\pi }\right).$

The value of $\sum _{K=1}^7{\tan }^2\left(\frac{K\mathrm{\pi }}{16}\right)$ is

If $ABCD$ is a quadrilateral then ${\sec }^2\left(\frac{A+B}{4}\right)-{\cot }^2\left(\frac{C+D}{4}\right)=?$

Find the value of $\frac{\sin 135°-\cos 120°}{\sin 135°+\cos 120°}$.

The value of $\cos \left(-{870}^0\right)$ is

Find the value of $\cos \left(390°\right)$.

Find the value of $\sin \left(405°\right)$

Find the value of $\cos \left(330°\right)$.

Find the value of $\sin \left(315°\right)$

What is the difference between the product of $\sin \left(\frac{\mathrm{\pi }}{2}\right), \sin \left(\frac{3\mathrm{\pi }}{2}\right)$ and product of $\cos \left(\frac{5\mathrm{\pi }}{6}\right), \cos \left(\frac{7\mathrm{\pi }}{6}\right)$.

Find the value of $\sec 210°$.

What is the value of $2\sin 75°\cos 75°$?

Evaluate: $\frac{1}{\sin \left(75°+\theta \right)}-\frac{1}{\cos \left(15°-\theta \right)}$