Grade 11Trigonometry
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)
1 Answer
Vikas TU
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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