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sinA+sinB=3. and cosA+cosB=4 find sin(A+B) and tan(A+ B)

sinA+sinB=3. and  cosA+cosB=4 
find sin(A+B)  and tan(A+ B)

Grade:11

3 Answers

divya
13 Points
5 years ago
sinA+sinB=3
2sin{(A+B)/2}cos{(A-B)/2}=3              
cosA+cosB=4
2cos{(A+B)/2}cos{(A-B)/2}=4            
on dividing by;we get
tan{(A+B)/2}=3/4
as we know tanQ={2tan(Q/2)}/{1-tan(Q/2)tan(Q/2)}
now putting Q=A+B,we will get the value of tan(A+B)
 also tanQ=sinQ/(1-sinQsinQ) thus from the you can find the value of sin(A+B)
 
abhignya
19 Points
5 years ago
a = 5 , b=6 ,sinA=5/6 then B =
 
divya
13 Points
5 years ago
in this question,sinA+sinB=3    (given)
therefore,when sinA=5/6
sinB=3 – 5/6=13/6
B=sin-1(13/6)

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