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

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

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
cosA + cosB =1/2 & sinA+ sinB = 1/4 
now cosA + cosB = 2 cos(A +B)/2 cos(A-B)/2 = 1/2--------------(I) 
sinA + sinB = 2 sin(A+B)/2 cos(A- B)/2 = 1/4---------------(II) 
dividing (I) by (II) we have 
(cosA+cosB)/( sinA +sinB)= 1/2/1/4 = 2 
or cot( A+B)/2 = 2 
or tan (A+B)/2 = 1/2
 
Regards
Arun (askIITians forum expert)

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