1
The question contains an expression but not an equation. An expression cannot be solved.
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
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.
The identity for tan(theta) is sin(theta)/cos(theta).
Cos theta squared
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
Tan^2
cosine (90- theta) = sine (theta)
-Sin^(2)(Theta) + Cos^(2)Theta => Cos^(2)Theta - Sin^(2)Theta Factor (Cos(Theta) - Sin(Theta))( Cos(Theta) + Sin(Theta)) #Is the Pythagorean factors . Or -Sin^(2)Theta = -(1 - Cos^(2)Theta) = Cos(2)Theta - 1 Substitute Cos^(2)Thetqa - 1 + Cos^(2) Theta = 2Cos^(2)Theta - 1
1
cos2(theta) = 1 so cos(theta) = ±1 cos(theta) = -1 => theta = pi cos(theta) = 1 => theta = 0
The question contains an expression but not an equation. An expression cannot be solved.
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
COS squared Theta + SIN squared Theta = 1; where Theta is the angles measurement in degrees.
cos(t) - cos(t)*sin2(t) = cos(t)*[1 - sin2(t)] But [1 - sin2(t)] = cos2(t) So, the expression = cos(t)*cos2(t) = cos3(t)
cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1