Question

How do you multiply and simplify `(sinx+cscx)(sin^2x+csc^2x-1)`?

Answer 1

`(sinx+cscx)(sin^2x+csc^2x-1)=sin^3x+csc^3x`

Explanation:

Recall the identity

`(a+b)(a^2+b^2-ab)=a^3+b^3`

As `sinx xx cscx =1`, we can write

`(sinx+cscx)(sin^2x+csc^2x-1)` as

`(sinx+cscx)(sin^2x+csc^2x-sinx cscx)`

= `sin^3x+csc^3x`