Show the identity can be derived from a sum or a difference identity and the pythagorean identity?
cos(2a)=1−2sin2a
1 Answer
Jun 3, 2018
See explanation
Explanation:
Remember the angle sum identity
cos(x+y)=cos(x)cos(y)−sin(x)sin(y)
Now let
cos(a+a)=cos(a)cos(a)−sin(a)sin(a)
⇒cos(2a)=cos2(a)−sin2(a)
By the pythagorean trig identity
cos(2a)=(1−sin2(a))−sin2(a)
⇒cos(2a)=1−2sin2(a)←What we wanted to show