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If 3 tan theta tan phi=1, then prove tha...

If `3 tan theta tan phi=1`, then prove that 2 `cos (theta+phi)=cos (theta-phi)`.

Text Solution

Verified by Experts

Given, `3 tan theta tan varphi=1` or not `cot theta cot psi=3`
or `(cos theta cos varphi)/(Sin theta sin varphi)=(3)/(1)`
By componendo and dividendo, we get
`(cos theta cos varphi +sin theta sin varphi )/(cos theta cos varphi -sin thetasin varphi)=(3+1)/(3-1)`
or `(cos(theta-varphi))/(cos (theta+varphi))=2`
or `2cos(theta+varphi)=cos(theta-varphi)`
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