Question

Simplify and write the trig expression in terms of sin and cos

Answer 1

We have:

`cot(-x)cos(-x)+sin(-x)=-(1)/(f(x))`

Then we use trigonometric identities to change the negative sign of the trigonometric functions, so:

`-sin(x)-cot(x)cos(x)=-(1)/(f(x))`

We clear f(x):

`f(x)=(1)/(sin(x)+cot(x)cos(x))=(1)/(sin(x)+(cos(x))/(sin(x))cos(x))=(1)/(sin(x)+(cos^2(x))/(sin(x)))`

we simply what we can:

`f(x)=(1)/((sin^2(x)+cos^2(x))/(sin(x)))=sin(x)`

Thus, the correct answer is;

`f(x)=sin(x)`