Let f(x)=sin23⁡x−cos22⁡x and g(x)=1+12tan−1⁡|x|. Then the number of values of x in the interval [−10π, 8π] satisfying the equation f(x)=sgn⁡(g(x)) is _____.

g(x)=12tan−1⁡|x|+1 or     sgn⁡(g(x))=1 or     sin23⁡x−cos22⁡x=1 or    sin23⁡x=1+cos22⁡xwhich is possible if sin x = 1 and cos x = 0. Therefore,sin⁡x=1,x=2nπ+π2Hence, −10π≤2nπ+π2≤8π   or   −214≤n≤154 or  −5≤n≤3Hence, number of values of x = 9.