Using x instead of theta, cos2x/cosec2x + cos4x = cos2x*sin2x + cos4x
= cos2x*(sin2x + cos2x)
= cos2x*1 = cos2x
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4*cos2(theta) = 1 cos2(theta) = 1/4 cos(theta) = sqrt(1/4) = ±1/2 Now cos(theta) = 1/2 => theta = 60 + 360k or theta = 300 + 360k while Now cos(theta) = -1/2 => theta = 120 + 360k or theta = 240 + 360k where k is an integer.
Cos2 doesn't equal pi; Cos2 equals roughly -0.416 (with radians).
sec2(x) - tan2(x)= 1/cos2(x) - sin2(x)/cos2(x)= (1 - sin2(x)) / cos2(x)= cos2(x) / cos2(x)= 1
cos2x/cosx = 2cosx - 1/cosx
Given that theta is the angle with respect to the positive X axis of a line of length 1, then sin(theta) = Y and cos(theta) is X, with (X,Y) being the point at the end of the line. As theta sweeps from 0 to 360 degrees, or 0 to 2 pi radians, that point draws a circle of radius 1, with center at (0,0).Since X, Y, and 1 form the sides of a right triangle, where 1 is the hypotenuse, then the pythagorean theorem states that X2 + Y2 = 12. This means that sin2(theta) + cos2(theta) = 1.Tan(theta) is defined as sin(theta) divided by cos(theta), or Y / X. Since division by zero is a limiting invalidity, then tan(theta) is asymptotic to Y=0, having value of +infinity at theta = 90 or pi / 4, and -infinity at 270 or 3 pi / 4.