Grade 11Trigonometry
If cosA+ cosB =1/2. and SinA+ SinB =1/4. Then the value of TanA+B/2 is?
1 Answer
Arun
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
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
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