Question

Use sum and difference identity to evaluate tan 75

Answer 1

Well, we could use the sum identity to do
\[\tan \left( 45+30 \right)=\frac{ tan45+tan30 }{ 1-tan45tan30 }\]
Can you take it from there?

Answer 2

yes, and I got stuck at \[\frac{ \frac{ 2 }{ 2\sqrt{3}+1 } }{ 1-\frac{ 2 }{ 2\sqrt{3} } }\]

Answer 3

I think you might have done it wrong.

Answer 4

The tangent of 45 is 1. The tangent of 30 is 1/sqrt3.

Answer 5

Using your TAN identity you have
\[\tan(75) = \frac{ \tan(45)+\tan(30) }{ 1-\tan(45)\tan(30) }\]\[= \frac{ 1 + \frac{ 1 }{ \sqrt{3} } }{ 1- \frac{ 1 }{ \sqrt{3} }}\]\[= \frac{ \sqrt{3}+1 }{ \sqrt{3}-1 }\]