4) Express as a single trigonometric function:

sin *x*(tan *x* + cot *x*)

Guest Feb 2, 2020

edited by
Guest
Feb 2, 2020

#2**0 **

The answerer Guest is correct but let me make it clearer.

\(sin(x)(tan(x)+cot(x))\) "Express as a single trigonometric function"

\(tan(x)=\frac{sin(x)}{cos(x)}\) (1)

\(cot(x)=\frac{cos(x)}{sin(x)}\) (2)

Substitute (1) and (2) into the equation

\(sin(x)(\frac{sin(x)}{cos(x)}+\frac{cos(x)}{sin(x)})\)

Multiply

\((\frac{sin^2(x)}{cos(x)}+cos(x))\). Now write it as a single fraction

\((\frac{sin^2(x)+cos^2(x)}{cos(x)})\)

Pythagorean identity, \(sin^2(x)+cos^2(x)=1\) substitute

\(\frac{1}{cos(x)}\)

Notice that \(sec(x)=\frac{1}{cos(x)}\)

So \(sin(x)(tan(x)+cot(x))\)\(= sec(x)\)

.Guest Feb 3, 2020