SOLUTION: if csc x=3, 90 degrees< x < 180 degrees then, sin (x/2) cos (x/2) tan (x/2)

Question 1204691: if csc x=3, 90 degrees< x < 180 degrees
then,
sin (x/2)
cos (x/2)
tan (x/2)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Hint #1
When 90 < x < 180, leads to

Hint #2
90 < x < 180 has all sides cut in half to 45 < x/2 < 90
Angle x/2 is in quadrant 1 where all 6 trig functions are positive

Hint #3
The half angle identities are

However, keep the 2nd hint in mind, so we can drop the plus minus to write

Or once you know what sin(x/2) and cos(x/2) are, you can compute tangent like so

More trig identities can be found here
https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

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