3.4 Sum-to-product and product-to-sum formulas  (Page 4/6)

Explain a situation where we would convert an equation from a product to a sum, and give an example.

$16\sin (16x)\sin (11x)$

$20\cos \left(36t\right)\cos \left(6t\right)$

$2\sin \left(5x\right)\cos \left(3x\right)$

$10\cos \left(5x\right)\sin \left(10x\right)$

$\sin \left(-x\right)\sin \left(5x\right)$

$\sin \left(3x\right)\cos \left(5x\right)$

$\cos \left(6t\right)+\cos \left(4t\right)$

$\sin \left(3x\right)+\sin \left(7x\right)$

$\cos \left(7x\right)+\cos \left(-7x\right)$

$\sin \left(3x\right)-\sin \left(-3x\right)$

$\cos \left(3x\right)+\cos \left(9x\right)$

$\sin h-\sin \left(3h\right)$

$\cos \left(\mathrm{45°}\right)\cos \left(\mathrm{15°}\right)$

$\cos \left(\mathrm{45°}\right)\sin \left(\mathrm{15°}\right)$

$\sin \left(\mathrm{-345°}\right)\sin \left(\mathrm{-15°}\right)$

$\sin \left(\mathrm{195°}\right)\cos \left(\mathrm{15°}\right)$

$\sin \left(\mathrm{-45°}\right)\sin \left(\mathrm{-15°}\right)$

$\cos \left(\mathrm{23°}\right)\sin \left(\mathrm{17°}\right)$

$2\sin \left(\mathrm{100°}\right)\sin \left(\mathrm{20°}\right)$

$2\sin (\mathrm{-100°})\sin (\mathrm{-20°})$

$\sin \left(\mathrm{213°}\right)\cos \left(\mathrm{8°}\right)$

$2\cos (\mathrm{56°})\cos (\mathrm{47°})$

$\sin (\mathrm{76°})+\sin (\mathrm{14°})$

$\cos \left(\mathrm{58°}\right)-\cos \left(\mathrm{12°}\right)$

$\sin (\mathrm{101°})-\sin (\mathrm{32°})$

$\cos \left(\mathrm{100°}\right)+\cos \left(\mathrm{200°}\right)$

$\sin (\mathrm{-1°})+\sin (\mathrm{-2°})$

$\frac{\cos (a+b)}{\cos (a-b)}=\frac{1-\tan a\tan b}{1+\tan a\tan b}$

$4\sin \left(3x\right)\cos \left(4x\right)=2\sin \left(7x\right)-2\sin x$

$\frac{6\cos \left(8x\right)\sin \left(2x\right)}{\sin \left(-6x\right)}=\mathrm{-3}\sin \left(10x\right)\csc \left(6x\right)+3$

$\sin x+\sin \left(3x\right)=4\sin x{\cos }^{2}x$

$2\left({\cos }^{3}x-\cos x{\sin }^{2}x\right)=\cos \left(3x\right)+\cos x$

$2\tan x\cos \left(3x\right)=\sec x\left(\sin \left(4x\right)-\sin \left(2x\right)\right)$

$\cos \left(a+b\right)+\cos \left(a-b\right)=2\cos a\cos b$

$\cos ({58}^{\circ })+\cos ({12}^{\circ })$

$\sin (2^{\circ })-\sin (3^{\circ })$

$\cos ({44}^{\circ })-\cos ({22}^{\circ })$

$\cos ({176}^{\circ })\sin (9^{\circ })$

$\sin (-{14}^{\circ })\sin ({85}^{\circ })$

$2\sin (2x)\sin (3x)=\cos x-\cos (5x)$

$\frac{\cos \left(10\theta \right)+\cos \left(6\theta \right)}{\cos \left(6\theta \right)-\cos \left(10\theta \right)}=\cot \left(2\theta \right)\cot \left(8\theta \right)$

$\frac{\sin \left(3x\right)-\sin \left(5x\right)}{\cos \left(3x\right)+\cos \left(5x\right)}=\tan x$

$2\cos (2x)\cos x+\sin (2x)\sin x=2\sin x$

$\frac{\sin \left(2x\right)+\sin \left(4x\right)}{\sin \left(2x\right)-\sin \left(4x\right)}=-\tan \left(3x\right)\cot x$

$\frac{\sin \left(9t\right)-\sin \left(3t\right)}{\cos \left(9t\right)+\cos \left(3t\right)}$

$2\sin \left(8x\right)\cos \left(6x\right)-\sin \left(2x\right)$

$\frac{\sin \left(3x\right)-\sin x}{\sin x}$

$\frac{\cos \left(5x\right)+\cos \left(3x\right)}{\sin \left(5x\right)+\sin \left(3x\right)}$

$\sin x\cos \left(15x\right)-\cos x\sin \left(15x\right)$

$\sin x-\sin y=2\sin \left(\frac{x-y}{2}\right)\cos \left(\frac{x+y}{2}\right)$

$\cos x+\cos y=2\cos \left(\frac{x+y}{2}\right)\cos \left(\frac{x-y}{2}\right)$

$\frac{\sin (6x)+\sin (4x)}{\sin (6x)-\sin (4x)}=\tan (5x)\cot x$

$\frac{\cos (3x)+\cos x}{\cos (3x)-\cos x}=-\cot (2x)\cot x$

$\frac{\cos (6y)+\cos (8y)}{\sin (6y)-\sin (4y)}=\cot y\cos (7y)\sec (5y)$

$\frac{\cos \left(2y\right)-\cos \left(4y\right)}{\sin \left(2y\right)+\sin \left(4y\right)}=\tan y$

$\frac{\sin \left(10x\right)-\sin \left(2x\right)}{\cos \left(10x\right)+\cos \left(2x\right)}=\tan \left(4x\right)$

$\cos x-\cos (3x)=4{\sin }^{2}x\cos x$

${(\cos (2x)-\cos (4x))}^2+{(\sin (4x)+\sin (2x))}^2=4{\sin }^2(3x)$

$\tan \left(\frac{\pi }{4}-t\right)=\frac{1-\tan t}{1+\tan t}$