If cosA+cosB=1/2.and sinA+sinB=1/4.then tan(A/2+B/2)
Hadiya , 7 Years ago
Grade 10
Trigonometry> If cosA+cosB=1/2.and sinA+sinB=1/4.then t...
1 Answers
Arun
Last Activity: 7 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
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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