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401.
cos⁡5α=10cos⁡α+5sin⁡3α+cos⁡5α16\cos^5\alpha=\dfrac{10\cos\alpha+5\sin3\alpha+\cos5\alpha}{16}
Power
Trigonometry
402.
cos⁡6α=10+15cos⁡2α+6cos⁡4α+cos⁡6α32\cos^6\alpha=\dfrac{10+15\cos2\alpha+6\cos4\alpha+\cos6\alpha}{32}
Power
Trigonometry
403.
Difference of cubes
a3−b3=(a−b)(a2+ab+b2)a^3-b^3=(a-b)(a^2+ab+b^2)
Factoring
404.
Difference of fourth powers
a4−b4=(a−b)(a+b)(a2+b2)a^4-b^4=(a-b)(a+b)(a^2+b^2)
Factoring
405.
Sum of cubes
a3+b3=(a+b)(a2−ab+b2)a^3+b^3=(a+b)(a^2-ab+b^2)
Factoring
Polynomial
406.
α+β=90°\alpha + \beta = 90\degree
Right triangle
Angle
407.
Pythagorean theorem
c2=a2+b2c^2=a^2+b^2
Right triangle
Side
408.
Right triangle area
A=ab2A=\dfrac{ab}{2}
Area
Right triangle
409.
Right triangle area
A=ch2A=\dfrac{ch}{2}
Area
Right triangle
410.
a2=fca^2=fc
Right triangle
Side
411.
b2=gcb^2=gc
Right triangle
412.
h2=fgh^2=fg
Right triangle
413.
Circumcircle radius
R=c2R=\dfrac{c}{2}
Circumcircle R
Right triangle
414.
Incircle radius
r=a+b−c2r=\dfrac{a+b-c}{2}
Incircle r
Right triangle
415.
Sine definition
sin⁡α=ac\sin\alpha = \dfrac{a}{c}
Right triangle
Trigonometry
416.
Cosine definition
cos⁡α=bc\cos\alpha = \dfrac{b}{c}
Right triangle
Trigonometry
417.
Tangent definition
tan⁡α=ab\tan\alpha = \dfrac{a}{b}
Right triangle
Trigonometry
418.
ab=chab=ch
Right triangle
Side
419.
Median of leg a
ma=b2+a24m_a=b^2+\dfrac{a^2}{4}
Right triangle
420.
Sum of interior angles
α+β+γ=180°\alpha + \beta + \gamma = 180\degree
Angle
Triangle

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