Show the identity can be derived from a sum or a difference identity and the pythagorean identity?

cos(2a)=12sin2a

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 x=y=a

cos(a+a)=cos(a)cos(a)sin(a)sin(a)

cos(2a)=cos2(a)sin2(a)

By the pythagorean trig identity cos2(a)=1sin2(a)

cos(2a)=(1sin2(a))sin2(a)

cos(2a)=12sin2(a)What we wanted to show