Question

Find the exact value using sum and difference formulas:
tan75

Answer 1

try tan(75) = tan(30 + 45)

and using the general for for the sum in tan its

\[\tan(A +B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A)\tan(B)}\]

both angles have exact values...

hope this helps.

Answer 2

I keep getting stuck after I plug everything in and write their real values

Answer 3

ok so

\[\tan(30) = \frac{1}{\sqrt{3}}...and....\tan(45) = 1\]

so you get

\[\frac{\frac{1}{\sqrt{3}} + 1}{1 - \frac{1}{\sqrt{3}} \times 1}\]

so it looks like you have

\[\frac{1 + \sqrt{3}}{\sqrt{3}} \div \frac{\sqrt{3} -1}{\sqrt{3}}\]

flip and multiply since you are dividing by a fraction gives

\[\frac{1 + \sqrt{3}}{\sqrt{3} -1}\]

I'd say you would need to rationalize the denominator to get the final answer.

Answer 4

thank you :)

Answer 5

glad to help