Find the Area of a segment of a circle if

Use an expression for $\frac{\sin (5\theta )}{\sin (\theta )}$ to find the roots of the equation $x^4-3x^2+1=0$ in trigonometric form

Verify the identity:
${\displaystyle \frac{(\cot \left(\theta \right)+1)(\cot \left(\theta \right)+1)}{\csc \theta }=\csc \left(\theta \right)+2\cos \left(\theta \right)}$

Given the cone ${\displaystyle z=\sqrt{x^2+y^2}}$ and the plane z=5+y.
Represent the curve of intersection of the surfaces with a vector function r(t).

Triangles ABC and DEF are right triangles, as shown. ${\displaystyle \mathrm{△}ABC}$ is similar to ${\displaystyle \mathrm{△}DEF}$.
Which ratios are equal to ${\displaystyle \cos \left(B\right)}$ ? Choose the TWO ratios that apply.

triangle ABC is a right triangle with its right angle at C. The bisector of angle B intersects AC at D. The bisector of the exterior angle at B intersects AC at E. If BD= 15 and BE=20, what are the lengths of triangle ABC?

The value of ${\tan }^{-1}\left(\frac{1}{\sqrt{2}}\right)-{\tan }^{-1}\left(\frac{\sqrt{5-2\sqrt{6}}}{1+\sqrt{6}}\right)$
is equal to
$\frac{\pi }{6}$
$\frac{\pi }{4}$
$\frac{\pi }{3}$
$\frac{\pi }{12}$

${\displaystyle \frac{\sin (a-b)}{\cos a}\cos b=\tan a-\tan b}$