Question

How do you multiply and simplify `(sinx-cosx)(sinx+cosx)`?

Answer 1

`2sin^2 x - 1`

Explanation:

This is simply a pair of binomials to be multiplied, The sum and difference rule here gives the answer as the square of the first term mimus the square of the second term. i.e.
`sin^2 x - cos^2 x` .
= `2sin^2 x` - 1 .... using the identity `cos^2 x + sin^2 x` = 1