How would you solve cos(5x)=sin(10x) ?

We will use double angle identities:
cos (5x ) = sin (10x )   
cos (5x ) = 2 cos (5x ) sin ( 5x )
cos ( 5 x) - 2 cos ( 5 x ) sin ( 5x ) = 0
cos ( 5 x ) · [ 1 - 2 sin (5 x) ] = 0
cos ( 5 x ) = 0                    or :       1 - 2 sin (5 x) = 0
5 x = π/2 +kπ,  k∈Z                        sin (5 x) = 1/2
x1 = π/10 + kπ/5                           5 x = π/6+2kπ    , k∈ Z
                                                       5 x = 5π/6 +2kπ , k∈ Z
                                                       x 2 = π/30 +2kπ/5
                                                       x 3 = π/9  + 2kπ/5

Look i don’t know the answer to this but someone else will so just wait a little bit longer