inverse trigonometric function

Aug 2011
125
1
Sir / Madam,

In the following problem:

solve:

Cos(tan-1x) = Sin[cot-1(3/4)]


In the above said problem, I proceeded

sin[(Pi/2) - tan-1x] = Sin[cot-1(3/4)]

(Pi/2) - tan-1x = cot-1(3/4)

Cot-1x = cot-1(3/4)

x = 3/4

However, they have given x = + 3/4 or - 3/4

How to identify it has two answers?

How to find the second answer.

Kindly enlighten me.

with warm regards,

Aranga