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Let A,B,C be the three angles such that ...

Let A,B,C be the three angles such that `A+B+C=pi , tan A.tan B=2`, then find the value of `(cos A cos B)/(cos C)`

Text Solution

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Given, `tan A.tan B=2`
`y=(cos A cos B)/(cos C)=-(cos A.cosB)/(cos(A+B))`
`(because cos C=cos(pi-(A+B)=-cos(A+B))`
`=(cos A.cosB)/(sin A sin B-cos A cos B)`
`=(1)/(tan A tan B-1)=(1)/(2-1)=1`
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