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If cos e cA+secA=cos e c B+s e cB , prov...

If `cos e cA+secA=cos e c B+s e cB ,` prove that: `"tanAtanB"=cot(A+B)/2`

Text Solution

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`co sec A+secA=co secB+secB`
or `(1)/(sinA)-(1)/(sinB)=(1)/(cosB)-(1)/(cosA)`
or `(sinB-sinA)/(sinA sinB)=(cosA-cosB)/(cos A cos B)`
or `(2sin((B-A)/(2))cos((A+B)/(2)))/(sinA sinB)=(2sin((B-A)/(2))cos((A+B)/(2)))/(sinA cosB)`
or `(cos((A+B)/(2)))/(cos((A+B)/(2)))=(sinAsinB)/(cos A cos B)`
or `tan A tan B=cot((A+B)/(2))`
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