To prove: [tex]\cot x+\tan x=\sec x\csc x[/tex]
where [tex]x\neq \dfrac{\pi}{2}(2n-1)[/tex]
Using trigonometry formula:
[tex]\cot x=\dfrac{\cos x}{\sin x}[/tex]
[tex]\tan x=\dfrac{\sin x}{\cos x}[/tex]
[tex]\sec x=\dfrac{1}{\cos x}[/tex]
[tex]\csc x=\dfrac{1}{\sin x}[/tex]
Taking Left hand side
[tex]\Rightarrow \dfrac{\cos x}{\sin x}+\dfrac{\sin x}{\cos x}[/tex]
[tex]\Rightarrow \dfrac{\cos^2 x+\sin^2x}{\sin x\cos x}[/tex]
[tex]\Rightarrow \dfrac{1}{\sin x\cos x}[/tex] [tex]\because \cos^2 x+\sin^2x=1[/tex]
[tex]\Rightarrow \sec x\csc x[/tex]
Hence proved
