Cosine theorem: A 2 = B 2+C 2-2bc * COSA
sin(A+B)=sinC
sin(A+B)=sinAcosB+sinBcosA
sin(A-B)=sinAcosB+sinBcosA
sin2A=2sinAcosA
cos2a=2(cosa)^2- 1=(cosa)^2-(sina)^2= 1-2(sina)^2
tan2A=2tanA/[ 1-(tanA)^2]
(sinA)^2+(cosA)^2= 1
Generally used to solve triangles is probably so much.
There seems to be no ready-made formula for probability.
Equal product method is often used to calculate the distance between points and surfaces in solid geometry. Construct a tetrahedron, and divide the volume calculated by another pair of bottom surfaces and heights by the distance between points and faces as the area of the bottom surface corresponding to the height.
Three perpendicular theorems are often used to calculate dihedral angles, or to construct them directly. The principle is easy to calculate, and each side of the constructed angle needs to be calculated for half a day, which is not worth the loss.
There seems to be no ready-made formula for conic curves, but there are some commonly used methods, such as setting points and eliminating points, or calculating ellipses with parametric equations.
The order is simpler. Generally, just find the general term and then prove the inequality. Inequalities can't be proved every time. I can't guarantee that the common method of general terms is to change the subscript, such as Sn-S(n- 1)=an.
If you can't directly find the general term that you can try to find the reciprocal, it is likely to be easy to find.