CARNEGIE MELLON UNIVERSITY
Department of Mathematical Sciences
21-122 Exam 1 Formula Sheet

Note: These will be provided during the exam. You are responsible for any other formulas that you may need.

• $\sin A \cos B =\frac{1}{2} \left[ \sin(A-B) +\sin(A+B) \right]$
• $\sin A \sin B =\frac{1}{2} \left[ \cos(A-B) -\cos(A+B) \right]$
• $\cos A \cos B =\frac{1}{2} \left[ \cos(A-B) +\cos(A+B) \right]$
• $\int \sec ^n x \ dx = \frac{ \tan x \sec^{n-2} x}{n-1} + \frac{n-2}{n-1}\int \sec^{n-2} x \ dx$, $(n \neq 1)$
• $\int \csc^n x \ dx = -\frac{ \cot x \csc^{n-2} x}{n-1} + \frac{n-2}{n-1}\int \csc^{n-2} x \ dx$, $(n \neq 1)$
• $t=\tan(\frac{x}{2})$, $\cos x =\frac{1-t^2}{1+t^2}$, $\sin x=\frac{2t}{1+t^2}$, $dx=\frac{2}{1+t^2} dt$