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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 pass

2 Answers

Anish Singhal
askIITians Faculty 1192 Points
5 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

Arun
25750 Points
5 years ago
Dear Anish
 
You have done this wrong
 
sinA + sinB = ½
2 sin(A + B)/2 * cos (A – B)/2= ½
 
Now
 
cos A + cos B = ¼
2 cos(A + B)/2 * cos (A – B)/2 = ¼
 
Now divide both the equations
 
tan (A + B)/2 = 2
 
Regards
Arun

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