Answer:
Sin(2theta)= 2sintheta costheta
Cos(2theta) = 2cos²theta - 1
Cos(2theta) = 1 - 2sin²theta
Step-by-step explanation:
Sin(2theta) = Sin(theta+theta)
Sin(theta+theta)= sintheta costheta + costheta sintheta
Since costheta and sintheta are occurring twice in the addition
Sin(theta+theta)= 2sintheta costheta
Cos(2theta) = cos(theta+theta)
= costheta costheta - sintheta sintheta
= cos²theta - sin²theta ... 1
From sin²theta + cos²theta = 1
Sin²theta = 1 - cos²theta ... 2
Substituting 2 into 1
Cos(2theta) = cos²theta - (1 - cos²theta)
Cos (2theta) = cos²theta - 1 + cos²theta
Cos(2theta) = 2cos²theta - 1
Cos(2theta) = 1 - 2sin²theta
