Question

Find the exact value of the given expression
(pic)

Answer 1

tan A - tan B = (1 + tan A tan B)tan(A - B)

Answer 2

so put the values n let me knw the answer

Answer 3

@aajugdar That identity doesn't help alot in this case. They key still is to find tan(A) an tan(B) which you must do either way.

Answer 4

i got .0641

Answer 5

okay? then?

Answer 6

see,she got the answer

Answer 7

is it the right answer though?

Answer 8

Not really!
Try not to use a calculator.
Use the identity and find the actual angle in terms of pi.
Only at the last step would you use the calculator (if necessary).

Answer 9

i dont know how to do that though. I suck at identities and ive tried so many times

Answer 10

The key is to compare
tan (A - B) = (1 + tan A tan B)tan(A - B)
with the given expression, and try to find what is A and what is B.
After that, your answer would be simply tan(A-B).

Answer 11

oops, it should read:
tan (A - B) = (tan(A)-tan(B))/(1+tan(A)tan(B))

Answer 12

i got 1/√3 but that isnt an answer choice

Answer 13

Your answer is correct, but note that 1/sqrt(3) is the same as sqrt(3)/3.
Perhaps the latter is one of the choices.

Answer 14

ok that was one of the choices, thanks!

Answer 15

\[\frac{ \tan \frac{ 17\pi }{12 }-\tan \frac{ \pi }{ 4 } }{ 1+\tan \frac{ 17\pi }{ 12 }\tan \frac{ \pi }{ 4 } }\]
\[=\tan \left( \frac{ 17\pi }{ 12 }-\frac{ \pi }{4 } \right)=\tan \frac{ 14\pi }{12 }\]
\[=\tan \frac{ 7\pi }{6 }=\tan \left( \pi+\frac{ \pi }{ 6} \right)=\tan \frac{ \pi }{6 }\]
now you can the solution.