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If sin A + sin B= C, cos A + cos B=D, then value of sin(A+B)

If sin A + sin B= C, cos A + cos B=D, then value of sin(A+B)

Grade:11

1 Answers

Vikas TU
14149 Points
3 years ago
Given that SinA+sinB=C  1 
cosA+cosB=D 2 
By utilizing change, 
from 1, 
2sin(A+B/2)cos(A-B/2)=C 
what's more, from 2, 
2cos(A+B/2)cos(A-B/2)=D 
Presently partitioning 1 and 2, we get 
tan(A+B/2)=C/D 
sin(A+B)= 2tan(A+B/2)/1+tan^2 (A+B/2) 
= 2CD/(C^2+D^2) 

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