Solve #sin^-1(x) - cos^-1(x) = sin^-1(3x+1)# ?

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Answer 1 · 2017-02-06T09:40:11

See below.

#sin^-1(x) - cos^-1(x) = sin^-1(3x+1)# so

#sin(sin^-1(x) - cos^-1(x))=sin(sin^-1(3x+1))#

but #sin(a-b)=sina cosb-cosasinb# so

#sin(sin^-1(x) - cos^-1(x))=sin(sin^-1(x))cos(cos^-1(x))-cos(sin^-1(x))sin(cos^-1(x))# so

#x^2-(sqrt(1-x^2))^2=3x+1# or

#x^2-1+x^2=3x+1# and solving we get at

#x=-1/2# which is the feasible solution.