If `costheta=cosalphacosbeta` , prove that `t a n(theta+alpha)/2t a n(theta-alpha)/2=t a n^2beta/2` .

Explanation

Given,

`costheta=cosalphacosbeta`

`∴cosbeta=(cosalpha)/(costheta)->(1)`

R.H.S

`=>tan^2(beta/2)=(1−cosbeta)^2/(sin^2beta)`

`⇒tan^2(beta/2)=((1−cosbeta)^2)/(1−cos^2beta)=((1−cosbeta)^2)/((1−cosbeta)(1+cosbeta))`

`⇒tan^2(beta/2)=(1−cosbeta)/(1+cosbeta)`

`=>tan^2(beta/2)=(1−(costheta)/(cosalpha))/(1+(costheta)/(cosalpha))`

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