Question

Sin(A+B)/sin A cos B = 1 + cot A tan B how to verify the identity?

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the identities

sin(A + B) = sinAcosB + cosAsinB

cotA = $\frac{cosA}{sinA}$ , tanA = $\frac{sinA}{cosA}$

Consider the left side

$\frac{sin(A+B)}{sinAcosB}$

= $\frac{sinAcosB+cosAsinB}{sinAcosB}$

= $\frac{sinAcosB}{sinAcosB}$ + $\frac{cosAsinB}{sinAcosB}$

= 1 + $\frac{cosA}{sinA}$ . $\frac{sinB}{cosB}$

= 1 + cotA tanB = right side , thus verified