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If (costheta=cosalphacosbeta , prove tha...

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

Text Solution

Verified by Experts

Given,
`cos theta=cos alpha cos beta`. We have
`cos beta=(cos theta)/(cos alpha)`
Now, `tan^(2)""(beta)/(2)=(1-cos beta)/(1+cos beta)=(1-(costheta)/(cos alpha))/(1+(cos theta)/(cos alpha))`
`=(2sin""(alpha+theta)/(2)sin""(theta-alpha)/(2))/(2cos ""(theta+alpha)/(2)cos ""(theta-alpha)/(2))`
`tan ""(theta+alpha)/(2) tan ""(theta-alpha)/(2)`
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