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Ray Of Light [21]
3 years ago
6

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

Mathematics
1 answer:
vlada-n [284]3 years ago
6 0

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

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