Question

1. csc(x)tan(x)=sec(x)proof both sides are equal

Answer 1

The equation is correct as both sides are equal

Step-by-step explanation:
`\csc \mleft(x\mright)\tan \mleft(x\mright)=\sec \mleft(x\mright)​`

csc(x) = cosec(x) = 1/sin x

`\begin{gathered} \csc \mleft(x\mright)\tan \mleft(x\mright)=(1)/(\sin x)*\tan \text{ x} \\ =\text{ }\frac{\tan \text{ x}}{\sin \text{ x}} \end{gathered}`

tan x = sinx/cos x

`\begin{gathered} \csc \mleft(x\mright)\tan \mleft(x\mright)=\frac{1}{\sin\text{ x}}*\frac{\sin \text{ x}}{\text{cos x}} \\ \csc (x)\tan (x)=\frac{1}{\cos \text{ x}} \end{gathered}`
`\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}`