Notes: Prove that sin(x)+sin(x)cot^2(x)=csc(x)

Saturday, May 23, 2015

We'll factor sin x and we'll
get:

$\displaystyle{\sin{{x}}}\cdot{\left({1}+{{\cot}}^{{2}}{x}\right)}={\csc{}}$
x

From Pythagorean identity, we'll
get:

$\displaystyle{1}+{{\cot}}^{{2}}{x}=\frac{{1}}{{{{\sin}}^{{2}}}}$
x)

We'll re-write the
expression:

$\displaystyle{\sin{{x}}}\cdot{\left(\frac{{1}}{{{{\sin}}^{{2}}{x}}}\right)}={\csc{}}$
x

We'll simplify and we'll
get:

$\displaystyle\frac{{1}}{{\sin{{x}}}}={\csc{}}$
x

Since the result represents a basic
identity, then the given expression represents an identity,
too.

Notes