Question

Please help! Use the formulas for functions of the difference and sum of two angles to find tan15degrees (using 45degrees and 30degrees)
a. (sqrt3-3)/(sqrt3+3)
b. (3-sqrt3)/(3+sqrt3)
c. (3+sqrt3)/(3-sqrt3)
d. (sqrt3+3)/(sqrt3-3)

Answer 1

tan45-tan15

Answer 2

tan45-tan30

Answer 3

\[\tan(15) = \tan(45-30) = \frac{\tan(45) -\tan(30)}{1+\tan(45)\tan(30)}\]

Answer 4

tan(45) = 1
tan(30) = sin(30)/cos(30) = (1/2) / sqrt3/2 = 1/sqrt3

Answer 5

did that help...do you know the answer now

Answer 6

I got a. Can you please clarify? @dumbcow

Answer 7

it can't be A because tan(15) is positive
both options A and D give negative answers

i used the difference formula for tangent function
i obtained values for tan(45) and tan(30) from unit circle
then just plug them into formula and simplify it into single fraction

Note: to get the answer they want....rationalize the denominator
\[\frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}\]
\[\rightarrow \frac{1-\frac{\sqrt{3}}{3}}{1+\frac{\sqrt{3}}{3}}\]

Answer 8

b.! THANKS SO MUCH