The product of two Trigonometrical functions I have the question: Express the following as the product of two trigonometrical functions: $$\sin(4 \theta) - 6 \sin(6 \theta)$$ Here is my attempt, is this correct ? !enter image description here

Using that

$$\sin (2a)=2\sin (a)\cos (a) $$ and $$\sin (3b)=3\sin(b)-4\sin^3 (b) $$

we find $$\sin (4t)=2\sin (2t)\cos (2t) $$ and $$\sin (6t)=3\sin(2t)-4\sin^3(2t) $$ the difference gives

$$\sin (2t)(2\cos (2t)-3+4(1-\cos^2 (2t)) $$ $$=\sin (2t)\left(4\cos^2 (2t)+2\cos (2t)+1\right) $$