How do you simplify #Cos(sin^-1 u + cos^-1 v)#?

1 Answer
Apr 13, 2016

#v*sqrt(1-u^2)-u*sqrt(1-v^2)#

Explanation:

#cos(sin^(-1)u+cos^(-1)v)=#

Making
#sin^(-1)u=alpha# => #sin alpha=u#
#cos^(-1)v=beta# => #cos beta=v#

And using the formula

#cos(alpha+beta)=cosalpha*cosbeta-sinalpha*sinbeta#

We get

#cos(alpha+beta)=sqrt(1-sin^2alpha)*cosbeta-sinalpha*sqrt(1-cos^2beta)#
#=sqrt(1-u^2)*v-u*sqrt(1-v^2)#
#=v*sqrt(1-u^2)-u*sqrt(1-v^2)#