Question

Suppose that tan(x)csc(x)=1/f(x).Write f(x) in terms of sin(x) and cos(x).f(x)=

Answer 1

Trigonometry

We are given the equation:

`\tan (x)\csc (x)=(1)/(f(x))`

It's required to write f(x) in terms of the sine and cosine functions.

Taking the reciprocal of both sides of the equation:

`f(x)=(1)/(\tan (x)\csc (x))`

Recall:

`\begin{gathered} \tan (x)=(\sin (x))/(\cos (x)) \\ \text{csc(x)}=(1)/(\sin (x)) \end{gathered}`

Substituting:

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

Simplifying:

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

Thus:

f(x)= cos(x)