I know that there is a trig identity for $\cos(a+b)$ and an identity for $\cos(2a)$, but is there an identity for $\cos(ab)$? $\cos(a+b)=\cos a \cos b -\s...

While finding the length of a curve, we assume an infinitesimal right triangle, of width $dx$ and height $dy$, so arc length is ${\sqrt{dx^2 + dy^2}}$. Bu...

I have this differentiation problem, taken from James Stewart's Calculus Early Transcendentals, 7th Ed. Page 205, Exercise 9. Find the derivative of ...

For instance let $$A=\begin{pmatrix} 3 & -1 & -1 \\ 2 & 1 &-2 \\ 0 & -1 & 2 \\ \end{pmatrix}$$ be a matrix and $$u_1=\begin{pmatri...

ps: I have asked this question on https://tex.stackexchange.com/ (here) but is regarded as off-topic. So I moved it here. I have seen different ways in pa...

This question is related, but different, to one of my previous questions (Does this infinite geometric series diverge or converge?). To avoid the previous...

A population of voters contains 40% Republicans and 60% Democrats. It is reported that 30% of the Republicans and 70% of the Democrats favor an election i...

Please help me by showing alternate methods to solve this complex number SAT question I encountered this question in one of my SAT practice tests. I know ...

I have the point $(1,1,1)$ and the plane $2x+2y+z = 0$. I want to find a point that is closest to my point on the plane. In other words, I want to find a ...

Solving for the tangent of an inverse secant function Hello, I am trying to evaluate this expression but haven't figured out how... $$\tan(\sec^{-1}(...