The equation is correct as both sides are equal
Explanation:[tex]\csc \mleft(x\mright)\tan \mleft(x\mright)=\sec \mleft(x\mright)[/tex]csc(x) = cosec(x) = 1/sin x
[tex]\begin{gathered} \csc \mleft(x\mright)\tan \mleft(x\mright)=\frac{1}{\sin x}\times\tan \text{ x} \\ =\text{ }\frac{\tan \text{ x}}{\sin \text{ x}} \end{gathered}[/tex]tan x = sinx/cos x
[tex]\begin{gathered} \csc \mleft(x\mright)\tan \mleft(x\mright)=\frac{1}{\sin\text{ x}}\times\frac{\sin \text{ x}}{\text{cos x}} \\ \csc (x)\tan (x)=\frac{1}{\cos \text{ x}} \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{\cos \text{ x}}=\text{ sec x} \\ \text{This means both sides of the equation are equal} \\ \csc (x)\tan (x)=\text{ sec(x)} \end{gathered}[/tex]
