Trigonometric Calculus

Question

If $$f(x) = 2 \sin x \cos x + \sin x,$$ evaluate $f(-\frac{\pi}{4})$.

The answer suggests $$-\frac{{2+\sqrt{2}}}{2}$$ but I am clueless on the procedures to get to the answer. Help please!

Answer 1

Notice that you can write $f(x)$ on this form

$$f(x)=\sin(2x)+\sin x$$ and the result follows knowing that $$\sin\left(\frac{-\pi}2\right)=-1\quad,\quad \sin\left(\frac{-\pi}4\right)=-\frac{\sqrt2}2$$