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If a, B, C are positive acute angles and...

If `a`, `B`, `C` are positive acute angles and `tanA=4/7`, `tanB=1/7`, `tanC=1/8`, prove that `A+B+C=45`

Text Solution

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`tan(A+B)=(tanA+tanB)/(1-tanAtanB)`
`((4/7)+(1/7))/(1-(4/49)`
`7/9`
`tan(A+B+C)=(tan(A+B)+tanC)/(1-tan(A+B)tanC`
`((7/9)+(1/8))/(1-7/72)`
`65/65=1`
`tan(A+B+C)=1=tan(45^o)`
`A+B+C=45^o`.
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