Question

Using the sum or difference identities, find the exact value for tan (75 degrees)

Answer 1

\[\large \tan (75^o)=\tan(30^o+45^o)\]
From here we can apply the Angle Sum Formula for Tangent,\[\large \tan(a+b)=\frac{\tan a+\tan b}{1-\tan a\cdot \tan b}\]

Answer 2

\[\large \tan(30^o+45^o)=\frac{\tan30^o+\tan45^o}{1-\tan30^o \cdot \tan45^o}\]

Answer 3

From here you just need to remember a couple special angles. Plug some stuff in, and simplify!

Answer 4

How did you know to add the numerator and subtract the denominator?

Answer 5

These are the Angle Sum and Difference Formulas for Tangent,\[\large \tan(a+b)=\frac{\tan a+\tan b}{1-\tan a\cdot \tan b}\]
\[\large \tan(a-b)=\frac{\tan a-\tan b}{1+\tan a\cdot \tan b}\]
How did I know? :o Because that's what the.... formula says .. to do :D

Answer 6

Oh! Thanks!