Use the fundamental identities and algebraic techniques to p

Use the fundamental identities and algebraic techniques to prove the following identities.

Use the fundamental identities and algebraic techniques to prove the following sin^4 theta - cos^4 theta = sin^2 theta - cos^2 theta

Solution

sin⁴theta - cos⁴theta

(sin²theta)²-(cos²theta)²

This is of the form a²-b² which is equal to (a+b)(a-b)

(sin²theta + cos²theta)(sin²theta-cos²theta)

And sin²theta + cos²theta=1

So we get

(1)(sin²theta-cos²theta) = sin²theta-cos²theta