Sin(cosx)=0 find x

When cosx = 0 , sin(cos(x)) will = 0

And cosx = 0  at  pi/2 and 3pi/2   (restricting ourselves to [0,2pi])

Here's a graph of the function......https://www.desmos.com/calculator/qafzzoaiad

Find the invSin of both sides:

invSin( sin ( cos (x) ) ) = invSin( 0 )

cos(x)  =  0

Find the invCos of both sides:

invCos( cos(x) )  =  invCos( 0 )

x  =  90° or 270°  (and suitable multiples)