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401.
$\cos^5\alpha=\dfrac{10\cos\alpha+5\sin3\alpha+\cos5\alpha}{16}$
Power
Trigonometry
402.
$\cos^6\alpha=\dfrac{10+15\cos2\alpha+6\cos4\alpha+\cos6\alpha}{32}$
Power
Trigonometry
403.
Difference of cubes
$a^3-b^3=(a-b)(a^2+ab+b^2)$
Factoring
404.
Difference of fourth powers
$a^4-b^4=(a-b)(a+b)(a^2+b^2)$
Factoring
405.
Sum of cubes
$a^3+b^3=(a+b)(a^2-ab+b^2)$
Factoring
Polynomial
406.
$\alpha + \beta = 90\degree$
Right triangle
Angle
407.
Pythagorean theorem
$c^2=a^2+b^2$
Right triangle
Side
408.
Right triangle area
$A=\dfrac{ab}{2}$
Area
Right triangle
409.
Right triangle area
$A=\dfrac{ch}{2}$
Area
Right triangle
411.
$b^2=gc$
Right triangle
412.
$h^2=fg$
Right triangle
413.
Circumcircle radius
$R=\dfrac{c}{2}$
Circumcircle R
Right triangle
414.
Incircle radius
$r=\dfrac{a+b-c}{2}$
Incircle r
Right triangle
415.
Sine definition
$\sin\alpha = \dfrac{a}{c}$
Right triangle
Trigonometry
416.
Cosine definition
$\cos\alpha = \dfrac{b}{c}$
Right triangle
Trigonometry
417.
Tangent definition
$\tan\alpha = \dfrac{a}{b}$
Right triangle
Trigonometry
419.
Median of leg a
$m_a=b^2+\dfrac{a^2}{4}$
Right triangle
420.
Sum of interior angles
$\alpha + \beta + \gamma = 180\degree$
Angle
Triangle

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