find f(2020π/9+2021kπ),where k is an integer number, f(x)=4sin^2 3x/2-4cos^2 3x/2
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Given : f(x)=4 sin square 3x/2- 4 cos square 3x/2.
To Find : f( 2020pi /9 +2021kpi ),
Solution:
f(x) = 4 sin² (3x/2) - 4 cos²(3x/2)
= - 4( cos²(3x/2) - sin² (3x/2))
= - 4 cos (3x)
= - 4 cos ( 3 (2020π /9 +2021kπ /9)
= - 4 cos ( (2020π /3 +2021kπ /3 )
= - 4 cos ( (672π + 4π /3 + 674kπ - kπ /3 )
= - 4 cos ( 4π /3 - kπ /3)
4π /3 = π + π/3
= - 4 cos ( -π /3 - kπ /3)
= - 4 cos ( k + 1)π/3
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