Trigonometric Equation - $\sin(a)+\cos(a)=1.2$

Question

$$\sin(a) + \cos(a) = 1.2 $$ Find $$\sin(a)\cdot\cos(a)$$

I honestly have no clue how to approach this problem. Some insight would be nice.

Answer 1

Hint

$$x+y=k \implies x^2+y^2+2xy=k^2.$$

Maybe in your case you know $x^2+y^2.$ And thus you can get $xy.$