Go to WEB-site https://keisan.casio.com/exec/system/1244946907 and use the Newton-Raphson method online calculator there. Input the given function in one window. Input its derivative 2*sin(x)*sinh(x) + 2*cos(x)*cosh(x) in the other window. Set up the number of iterations and the desired accuracy. Press the "Execute" button. You will get the solution in a second, with step-by-step printing. After 4 iterations, the found root is x = 0.4668337563 with 10 correct decimals.