Question

if cosec A+secA=cosecB+secB, prove that tanAtanB=cotA+B/2

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Here

cosec A+ secA =cosecB +sec B

or,1/sinA+1/cosA=1/sinB+1/cosB

or,1/sinA-1/sinB=1/cosB-1/cosA

or.(sinB-sinA)/sinAsinB=(cosA-cosB)/cosAcosB

or,sinAsinB/cosAcosB=(sinB-sinA)/(cosA-cosB)

or,tanAtanB=[2cos(A+B)sin(B-A)]/[-2sin{(A+B)/2]*[sin(A-B)/2}]

or,tanAtanB=[2cos(A+B)sin(B-A)]/[-2sin{(A+B)/2][-sin(B-A)/2]/

or,tanAtanB=cos[(A+B)/2]/[sin(A+B)/2]

          tanAtanB=cos(A+B)/2 

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