Question

Express as a product:

`4sin^2(a)-3`

Answer 1

(2sin(a) -√3)×(2sin(a) +√3)

Explanation:

One of the terms of the difference is a perfect square. So, we can use the form for factoring the difference of squares:

p² -q² = (p -q)(p +q)

Here, we can make the assignments ...

p = 2sin(a)

q = √3

Then we have ...

4sin²(a) -3 = (2sin(a))² -(√3)² = (2sin(a) -√3)(2sin(a) +√3)