---
cards-deck: default_obsidian
---

#math/calculus 


#math/calculus 

# trig identity
## basic

$sin^2x$ ::: $sin^2x+cos^2x=1$ ^1651675101678

$sin^2x$ halves ::: $sin^2x=1/2(1-cos{2x})$ ^1651675101686

$cos^2x$ ::: $\cos^2x=1/2(1+\cos{2x})$ ^1651674952732

$\sin x\cos x$ ::: $=\frac{1}{2}sin2x$ ^1651675101693

## $tan^{2}x + 1$
#card/reverse
$tan^{2}x  + 1 = sec^{2}x$
because: $\frac{sin^{2}x}{cos^{2}x} + \frac{cos^{2}x}{cos^{2}x} = \frac{1}{cos^{2}x}$
^1651675939328

## derivatives

$\frac{dx}{dy}\sec x$ ::: $\tan x \sec x$  ^1651677169665

$\frac{dx}{dy}\tan x$ ::: $\sec^{2}x$ ^1651679351621

$\frac{d x}{d y} \ln |x|$ ::: $\frac{1}{x}$ ^1652457023180

## integrals

$\int \sec x dx$ ::: $\ln |\sec x + \tan x|$ ^1651679351627

$\int \tan x dx$ ::: $\ln |\cos x|+C$ ^1652457023184

## crazy identities

$\sin A \cos B$ ::: $\frac{1}{2}(\sin(A-B)+\sin(A+B))$ ^1651679351632

$\sin A \sin B$ ::: $\frac{1}{2}(\cos(A-B)-\cos(A+B))$ ^1651679351636

$\cos A \cos B$ ::: $\frac{1}{2}(\cos(A-B)+\cos(A+B))$ ^1651679351639

$\csc^{2}x=$ ::: $=1+\cot^{2}x$ ^1652457023188