(2*sqrt3 + 4)/-2 = 2*sqrt3/-2 + 4/-2 =.........?
tanA + tanB is not equal to tan(A+B)
tan(A+B) = (tanA+tanB)/[1-tanA*tanB]
1) "The answer is supposed to be..."
That is what you have. Try some algebra. There is a reason why you studied "simplification" over and over and over.
2) What is the difference.
Simply, you do not understand the concept fo funciton notation.
f(a) is a function operating on a value 'a'.
f(b) is a function operating on a value 'b'.
f(a+b) is a function operating on the value 'a + b'.
f(a) + f(b) is ths sum of a function operating on a value 'a' and that same function operating on a value 'b'.
I am not encouraged that 1) You started the problem with the wrong expression and 2) you only got so far as to wonder "they give different answers". You really should start understanding what you are doing. One day you will discover the mathematics is not just a class to get through.
and also the following trigonometric identities
To start, draw 2 right-angled triangles.
For the first
So there is something wrong here as the opposite cannot be longer than the hypotenuse
since the hypotenuse is the longest side of a right-angled triangle.
Then, when you use Pythagoras' theorem, you find the 3rd side
and you can write
Do the same with the 2nd triangle, using
Again you get the 3rd side of that to help you write and
Draw the triangle.
Pythagoras' theorem gives
Use this to find the length of the 3rd side.
Finally use the trigonometric identity.
You need and also.
You get these when you have the 3rd side of the 2nd triangle.
gives you 2 of the 3 sides of that one.
Pythagoras theorem gets you the 3rd.
Then you can write and
before using the trigonometric identity.
well, once you have found out what
you find out the quadrant of the angle using the following...
gives the vertical co-ordinate of a point on the unit circle circumference, centred at (0,0).
gives the horizontal co-ordinate.
sin + and cos + is the 1st quadrant 0-90 degrees
sin + and cos - is the 2nd quadrant 90-180 degrees
sin - and cos - is the 3rd quadrant 180-270 degrees
sin - and cos + is the 4th quadrant 270-360 degrees