Working with trigonometric relationships in degreesTrigonometric identities
Trigonometric functions can have several solutions. Sine, cosine and tangent all have different positive or negative values depending on what quadrant they are in.
There are some trigonometric identities which you must remember in order to simplify trigonometric expressions when required.
These are:
\({\sin ^2}x + {\cos ^2}x = 1\)
And:
\(\tan A = \frac{{\sin A}}{{\cos A}}\)
Example
Prove that \({\cos ^3}x + {\sin ^2}x\cos x = \cos x\)
Answer
When you are asked to prove something, ignore the right hand side of the equals sign in your working as we are not just assuming that this statement is correct: we need to prove that it is!
Firstly, factorise the left hand side by taking out a common factor:
\({\cos ^3}x + {\sin ^2}x\cos x\)
\(= \cos x({\cos ^2}x + {\sin ^2}x)\)
\(= \cos x(1)\)
This is because \({\cos ^2}x + {\sin ^2}x = 1\)
\(= \cos x\)
Question
Prove that \(\frac{cosA+sinA}{cosA}=1+tanA\)
Remember that we are only dealing with the left hand side of this equation.