Simplify the expression csc(arccos(x)) step-by-step?

Question

8378 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-16T03:49:48

#csctheta=1/sqrt(1-x^2)#

.

#csc(arccos(x))#

#arccos(x)# means an angle whose cosine is #x#.

Let's call that angle #theta#. Then we can say:

#arccos(x)=theta#

#costheta=x#

The problem is asking us to find #csctheta#.

#costheta=x, :. cos^2theta=x^2, sin^2theta=1-cos^2theta=1-x^2, sintheta=sqrt(1-x^2)#

#csctheta=1/sintheta=1/sqrt(1-x^2)#