Inverse Trig (is this allowed) (1 Viewer)

[_ShiFTy_]

e.g. if the question asks show
tan-1 (3/4) + tan-1 (4/5) = some constant

Are we allowed to tan both sides, and then prove the LHS = RHS?

My teacher is adamant that this is not allowed, but surely it is, isnt it?

 

[Riviet]

You are allowed, and it is probably the best way to approach this type of question. Remember to always state the range of the inverse tan function; in your example, the constant is an angle, let it be theta, then the range of values would be in the interval 0 < theta < pi. With this in mind, you can then go about proving both sides equal.

 

[Mountain.Dew]

of course its allowed.

please, do not be intimidated with tan inverse (something) that doesnt appear nice. all those trig inverse are merely ANGLES, CONSTANTS.

you could also change the tan inverse to cos or sine inverse, merely by using a right angled triangle, then sin or cos both sides.

an elegant way to do it is this:

LHS = tan-1 (3/4) + tan-1 (4/5)
= tan^-1(tan(tan^-1(3/4) + tan^-1(4/5))]

and just simply do the expansions inside the first tan^-1 to get LHS = tan^-1(some constant)

 

[.ben]

are you allowed to integrate bot sides?

 

[Mountain.Dew]

are you allowed to integrate bot sides?

you are, bit u wont get anywhere... u'll simply get

[tan-1 (3/4) + tan-1 (4/5)]x + c = (some constant )x + d

that looks much worse than before...

remember LHS is merely a constant, not some variable.