How do you simplify tan(arccos(x/3))tan(arccos(x3))?

1 Answer
A. S. Adikesavan · 1s2s2p
Aug 2, 2016

sqrt (9-x^2)/x, -3<=x<=3√9−x2x,−3≤x≤3.

Explanation:

Let a = arccos (x/3) in Q1 or Q2, -1<=x/3<=1a=arccos(x3)∈Q1orQ2,−1≤x3≤1, and so, -3 <=x <= 3−3≤x≤3

Then, cos a = x/3, sin a = sqrt(1-cos^2 a)= sqrt(1-x^2/9)cosa=x3,sina=√1−cos2a=√1−x29,

Now, the given expression is

tan a =sin a/cos atana=sinacosa

=sqrt (9-x^2)/x,=√9−x2x,

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