Prove that $tan  x +cot  x=sec x  csc x$

Prove that $tan x +cot x=sec x  csc x$. 

Please show all the required work. 

Calculus Trigonometric Functions Algebra
Willyburns Willyburns
34
Report

Answer

\[\tan x + \cot x=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}=\frac{\sin ^2 x+\cos^2 x}{\sin x \cos x}\]
\[=\frac{1}{\sin x \cos x}=\frac{1}{\cos x} \cdot \frac{1}{\sin x}\]
\[=\sec x \csc x.\]

Erdos Erdos
4.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.