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
