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If sinA+sinB=1/2 and cosA+cosB=1/4 then prove that tan(A+B)/2=0

If sinA+sinB=1/2 and cosA+cosB=1/4 then prove that tan(A+B)/2=0

Grade:12th

2 Answers

Abhinav Gupta
77 Points
4 years ago
sinA+sinB=1/2so, 2sin(A+B)/2* cos(A-B)/2=1/2cosA+cosB=1/4so, 2cos(A+B)/2*cos(A-B)/2=1/4Dividing both equations,We get,tan(A-B)/2=2
Neha
17 Points
3 years ago
Sin A + sin B=1/2 
 Sin (A+B)=1/2
Cos A+ cos B =1/4
Cos (A+B)=1/4
Sin (A+B)/cos (A+B)=1/2×4/1=2
Sin (A+B)/cos (A+B)=tan(A+B)=2
Now dividing both sides by 2,we have
Tan(A+B)/2=2/2
Tan(A+B)/2=1
Tan (A+B)=1

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