Evaluate tan(tan^-1 (π/3) + (π/4) )
Makes no sense. I mean, tan^-1(π/3) is defined, but it is not one you come across very often. I suspect you meant
tan( (π/3) + (π/4) ) = (tan(π/3)+tan(π/4))/(1 - tan(π/3) tan(π/4))
= (√3 + 1)/(1 - √3 * 1)
= (1+√3)/(1-√3)
= (4+2√3)/(1-3)
= -2-√3
Or, just for fun, maybe you meant
tan(tan^-1(1/3) + tan^-1(1/4))
That would be
(1/3 + 1/4)/(1 - 1/3 * 1/4) = 7/11
tan^-1 mean tan inverse, π/3 or π/4 mean pi/3 + pi/4 respectively
I read that as
tan(tan^-1 [(π/3) + (π/4)] ) , see how important brackets are ?
= tan(tan^-1 [ 7π/12] )
which would simply be
7π/12
just like tan(tan^-1 (1/2) ) = 1/2
yes your are write
this what i got when i try it... tan( tan inverse (180/3+ 180/4) ) tan 89.4543 = 105°. am i right?
NO
π = 3.14159... not 180
whenever you see π floating around in trig problems, you can assume that
they are dealing with radians, not degrees.
If you wish to use your calculator for this question, then
π/3+π/4 = 1.832595....
now with your setting on degrees, press
2ndF tan to get 61.379...
now press tan to get 1.8325.. back again!! ,
which is your π/2+π/4 or 7π/12
try it with setting on RAD, same thing, although you get a different intermediate answer.
try it with setting on GRAD, same thing
So 105° is a silly answer.
thanks
To evaluate this expression, we will first simplify the expression inside the tangent function.
Let's start with the expression inside the parentheses, which is tan^(-1) (π/3) + (π/4).
The inverse tangent function (tan^(-1)) and tangent function (tan) are inverse functions of each other. So, when applied to the same argument, they cancel each other out and leave us with just the argument.
Therefore, tan(tan^(-1) (π/3) + (π/4)) simplifies to tan(π/3 + π/4).
Next, we use the trigonometric identity for the sum of angles in the tangent function, which states that tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)).
In this case, A = π/3 and B = π/4.
So, tan(π/3 + π/4) = (tan(π/3) + tan(π/4))/(1 - tan(π/3)tan(π/4)).
Now, let's find the values of tan(π/3) and tan(π/4).
The tangent of π/3 is √3, and the tangent of π/4 is 1.
Plugging these values into the expression, we get:
(tan(π/3) + tan(π/4))/(1 - tan(π/3)tan(π/4)) = (√3 + 1)/(1 - √3 × 1).
Simplifying further, we have:
(√3 + 1)/(1 - √3) = (√3 + 1)/(1 - √3) * (1 + √3)/(1 + √3)
Expanding this expression, we get:
(√3 + 1)(1 + √3)/(1 - √3)(1 + √3)
= (3 + 2√3 + √3 + 1) / (1 - 3)
= (4 + 3√3) / (-2)
= -(2 + √3)
Therefore, the value of the expression tan(tan^(-1) (π/3) + (π/4)) is -(2 + √3).