Question

Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.51tan- tani125r1 + tan(9)( 12 )tan (6)

Answer 1

Remember that

`\tan (a-b)=(\tan a-\tan b)/(1+\tan a\cdot\tan b)`

In this problem

a=5pi/12

b=pi/4

substitute

`\begin{gathered} \tan ((5\pi)/(12)-(\pi)/(4))=(\tan (5\pi)/(12)-\tan (\pi)/(4))/(1+\tan (5\pi)/(12)\cdot\tan (\pi)/(4)) \\ \\ \tan ((\pi)/(6))=\tan ((5\pi)/(12)-(\pi)/(4))=(\tan(5\pi)/(12)-\tan(\pi)/(4))/(1+\tan(5\pi)/(12)\cdot\tan(\pi)/(4)) \end{gathered}`

The answer is

`\tan ((\pi)/(6))`