Cos2 doesn't equal pi; Cos2 equals roughly -0.416 (with radians).
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sec2(x) - tan2(x)= 1/cos2(x) - sin2(x)/cos2(x)= (1 - sin2(x)) / cos2(x)= cos2(x) / cos2(x)= 1
Using x instead of theta, cos2x/cosec2x + cos4x = cos2x*sin2x + cos4x = cos2x*(sin2x + cos2x) = cos2x*1 = cos2x
Yes
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
it is pi rounded