Find the exact value of sin(tan^-1 1/2)?

What are the steps for this?

1 Answer
Mar 22, 2018

sin(arctan(12))=15

Explanation:

Let x=arctan(12).

Then x(0,π2) and:

tanx=12

sinxcosx=12

sin2xcos2x=14

sin2x1sin2x=14

4sin2x=1sin2x

5sin2x=1

sin2x=15

sinx=15

and we take the root with the positive sign because the angle is in the first quadrant.