Question

How to solve tan 195 using the sum and difference formula?

Answer 1

With magic. D'uh :D

Or... you could find two angles whose tangents you DO know, (say, 30 or 45) and that add up to 195.

Can you find two such angles?

Answer 2

its is 135 and 60 i believe?

Answer 3

Great ^_^
What are tan(135) and tan(60) ?

Answer 4

i got 1 for tan 135 and (square root)3/3 for 60

Answer 5

You might want to take a better look at tan(135) ... ^_^

Answer 6

is it -1

Answer 7

Yes... lol it's in the second quadrant, where ONLY sine and cosecant are positive, the rest should be negative.
What about tan(60) though?

Answer 8

i apoligize is it square root of 3?

Answer 9

Yes, it is ^_^
\[\large \tan(135^o) = -1\\\large \tan(60^o) = \sqrt 3\]

Now, we have..
\[\Large \tan(195^o) = \tan(\color{blue}{135^o} + \color{red}{60^o})\]

And the formula: \[\Large \tan(\color{blue}\alpha + \color{red}\beta ) = \frac{\tan(\color{blue}\alpha)+\tan(\color{red}\beta)}{1-\tan(\color{blue}\alpha)\tan(\color{red}\beta)}\]

Just plug in... and be done ;)

Answer 10

is it -1+(squareroot)3

Answer 11

over 1+\[1+\sqrt{3}\]

Answer 12

This?
\[\Large \frac{-1+\sqrt 3}{1+\sqrt3}\]

Answer 13

yes

Answer 14

It's correct. Well done ^_^

Answer 15

is it -4+2(squareroot)3/-2?

Answer 16

You rationalise denominators? lol We usually leave that as is...
Anyway, you're right, but you might as well multiply both the numerator and denominator by -1 so as to remove that ugly negative sign down below:
\[\Large \frac{4-2\sqrt3}{2}\]
And then just simplify ^_^

Answer 17

so is it 2-squareroot(3)

Answer 18

That is correct :)