Question

how do i prove the identity of tan x + cot x = 1/ sin x cos x?

Answer 1

\(\bf \color{blue}{tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}}\\ \quad \\ \quad \\

tan(x)+cot(x)\implies \cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{\square +\square }{{\color{red}{ lcd}}}\)

sum them up, see what you get

Answer 2

im not sure how to sum them up, i haven'tdone this type of math problems in 4 years

Answer 3

heh, ok...so.. what do you think is our LCD?

Answer 4

sinx cosx

Answer 5

\(\bf tan(x)+cot(x)\implies \cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \\ \quad \\\cfrac{[sin(x)sin(x)]+[cos(x)cos(x)]}{cos(x)sin(x)}\\ \quad \\
\cfrac{sin^2(x)+cos^2(x)}{cos(x)sin(x)}\qquad recall\implies{\color{blue}{ sin^2(\theta)+cos^2(\theta)=1}} \\ \quad \\
\cfrac{sin^2(x)+cos^2(x)}{cos(x)sin(x)}\implies \cfrac{1}{cos(x)sin(x)}\)