Question

Find the identical expression for cos(A+B) /sinAcosB

Answer 1

EXPLANATION

Apply the fraction rule:

$\frac{a\pm b}{c}=\frac{a}{c}\pm\frac{b}{c}$$\frac{\sin(a)+\sin(b)}{\sin(a)\cos(b)}=\frac{\sin(a)}{\sin(a)\cos(b)}+\frac{\sin (b)}{\sin (a)\cos (b)}$$=\frac{\sin(a)}{\sin(a)\cos(b)}+\frac{\sin (b)}{\sin (a)\cos (b)}$

Cancel:

$\frac{\sin (a)}{\sin (a)\cos (b)}$

Cancel the common factor: sin(a)

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