cos^-1(x)+cos^-1(2x)=3pi/4.Find the value of ‘x’.................................................................................

use the formula fof:
cos^-1 (A) + cos^-1 (B) = cos^-1 [AB – sqrt(1-A^2)sqrt(1 – B^2)]
we, get
x(2x) – sqrt(1 – x^2)sqrt(1 – (2x)^2) = cos(3pi/4) = -1/root(2)

now you can simpify by squaring and solving quadratic to get the value of x.

Thanks.