Question

Show one side can be simplified so it is identical to the other side. Is this problem correct? sec x cot x = csc x truesec (x) cot (x)= 1/sin(x)1/sin(x) = csc (x)= csc (x) true

Answer 1

We are given the following expression:

`\sec x\cot x`

In order to simplify this expression we will use the following relationship:

`\sec x=(1)/(\cos x)`

Replacing we get:

`\sec x\cot x=((1)/(\cos x))(\cot x)`

Now we will use the following relationship:

`\cot x=(\cos x)/(\sin x)`

Replacing we get:

`((1)/(\cos x))(\cot x)=((1)/(\cos x))((\cos x)/(\sin x))`

Now we cancel out the cosines of x:

`((1)/(\cos x))((\cos x)/(\sin x))=(1)/(\sin x)`

And this expression is equivalent to cosecant of "x", therefore:

`\sec x\cot x=\csc x`