Answered

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

Sagot :

Answer:

see explanation

Step-by-step explanation:

Using the identities

sin(A + B) = sinAcosB + cosAsinB

cotA = [tex]\frac{cosA}{sinA}[/tex] , tanA = [tex]\frac{sinA}{cosA}[/tex]

Consider the left side

[tex]\frac{sin(A+B)}{sinAcosB}[/tex]

= [tex]\frac{sinAcosB+cosAsinB}{sinAcosB}[/tex]

= [tex]\frac{sinAcosB}{sinAcosB}[/tex] + [tex]\frac{cosAsinB}{sinAcosB}[/tex]

= 1 + [tex]\frac{cosA}{sinA}[/tex] . [tex]\frac{sinB}{cosB}[/tex]

= 1 + cotA tanB = right side , thus verified

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