Question

How do you prove `cos 2theta = cos^(4)theta - sin^(4)theta`?

Answer 1

We can prove this from left hand side as well as right hand side.

Explanation:

We know that

`cos(2theta)=cos^2(theta)-sin^2(theta)`
`cos(2theta)= 1 *(cos^2(theta)-sin^2(theta))`
`cos(2theta)=(cos^2(theta)+sin^2(theta))(cos^2(theta)-sin^2(theta))` [since `sin^2theta+cos^2theta=1`]
`cos(2theta)=cos^4(theta)-sin^4(theta)` [since `(a+b)(a-b)=a^2-b^2`]

Hence proved