Question

Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.tan(80°) – tan (20)1 + tan(80°)tan (20

Answer 1

Okay, here we have this:

Considering the provided expression, we are going to use the tangent formula of a subtraction, and is the following:

`\tan (A-B)=(tan\mleft(A\mright)-tan\mleft(B\mright))/(1+tan\mleft(A\mright)tan\mleft(B\mright))`

We can see that the expression they provide us has the same form as that of the tangent of a subtraction, where A is equal to 80° and B is equal to 20°, so we obtain:

`\begin{gathered} (tan\left(80°\right)-tan\left(20°\right))/(1+tan\left(80°\right)tan\left(20°\right)) \\ =\tan (80\degree-20\degree) \\ =\tan (60\degree) \end{gathered}`

Finally we obtain that the original expression is equal to tan(60°).