Question

the value of (sin 7x + sin5x) /(cos 7x+cos 5x)(sin9x+sin3x)/(cos9x+cos3x) is​

Answer 1

Answer:

$\frac{\sin \left(7x\right)+\sin \left(5x\right)}{\cos \left(7x\right)+\cos \left(5x\right)}\cdot \frac{\sin \left(9x\right)+\sin \left(3x\right)}{\cos \left(9x\right)+\cos \left(3x\right)}=\frac{\left(\sin \left(7x\right)+\sin \left(5x\right)\right)\left(\sin \left(9x\right)+\sin \left(3x\right)\right)}{\left(\cos \left(7x\right)+\cos \left(5x\right)\right)\left(\cos \left(9x\right)+\cos \left(3x\right)\right)}$

Explanation:

$\frac{\sin \left(7x\right)+\sin \left(5x\right)}{\cos \left(7x\right)+\cos \left(5x\right)}\cdot \frac{\sin \left(9x\right)+\sin \left(3x\right)}{\cos \left(9x\right)+\cos \left(3x\right)}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}$

$=\frac{\left(\sin \left(7x\right)+\sin \left(5x\right)\right)\left(\sin \left(9x\right)+\sin \left(3x\right)\right)}{\left(\cos \left(7x\right)+\cos \left(5x\right)\right)\left(\cos \left(9x\right)+\cos \left(3x\right)\right)}$