I have to use induction to prove that for all nE N21 Li=1 (1+sin) My first thought is to price that this works when n-1, assume it is true, and then move on to n+1. exp(-1)-еxp (1). The problem is that sin). sin) becomes (1.1752011...)į but I am not sure 2i if that is larger than or equal to 1/20. I would like help on how to understand this part, and then also with the second step of induction please.

Please complete proof with all steps

The remaining problems require you to construct a mathematical proof by induction. Remember, if you don't make use of the inductive hypothesis, there is no way to finish the proof correctly! 9. The following formula is called De'Moivre's Formula: (cos+ i sin 0)" = cos(ne)+ i sin(ne) Prove De Moivre's formula for all integers n 20. (Hint: you will need a trig identity from Precalculus).

Verify that the given vector function satisfies the given system. 200 x=710 x, x(t)= 8 0 1 4et -3e" What is the rule for finding the derivative of a matrix A(t)? dA ○ A. dt (b) = A' (b) = ['₁ (%)] dA ○ B. dt (to) A' (to) IjA, where Iij is the ijth identity matrix. dA ос. (to) A' (to) [a' (to) xAj] dt dA = OD. (to) A (1)= [a' (to)] Find x'. x' = (Type an exact answer in terms of e.) How is the product of two matrices computed? ○ A. The product of two matrices A and B is formed by taking the array of dot products of the rows of the first "factor" A with the columns of the second "factor" B; the dot product of the ith row of A with the jth column of B is written as the ijth entry of the product AB. ○ B. The product of two matrices A and B is formed by multiplying the ijth entry in matrix A with the jith entry in matrix B. ○ C. The product of two matrices A and B is formed by multiplying the ijth entry in matrix A with the corresponding ijth entry in matrix B. ○ D. The product of two…