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Let theta ,phi in [0,2pi] be such that 2...

Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) cos phi -1, tan(2pi-theta) > 0 and -1 < sin theta < -sqrt3/2.` Then `phi` cannot satisfy

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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