Proving the identity \(\displaystyle{\frac{{{1}}}{{{\tan{{x}}}}}}+{\tan{{x}}}={\frac{{1}}{{{\sin{{x}}}{\cos{{x}}}}}}\) And here's what I've

Jazmyn Holden

Jazmyn Holden

Answered question

2022-03-30

Proving the identity 1tanx+tanx=1sinxcosx
And here's what I've solved for:
RHS=1sin(x)cos(x)+sin(x)cos(x)=cosxsinx+sin(x)cos(x)
Then, I get stuck. The answers section says the next step should be:
cos2(x)+sin2(x)sin(x)cos(x)=RHS

Answer & Explanation

Cason Singleton

Cason Singleton

Beginner2022-03-31Added 13 answers

Way of thinking: You want to simplify the more complicated side, which is the LHS, to a less complicated expression. You have two fractions with different denominators. So you multiply the numerator and denominators of the two fractions to obtain a common denominator.
1tanx+tanx=cosxsinx+sinxcosx=cos2xcosxsinx+sin2xsinxcosx=cos2+sin2xsinxcosx

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?