Question

If cosa+cosb=1/2 and sina+sinb=1/4 then find tan(a+b/2)

Answer 1

Answer:

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

Answer 2

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