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In triangleABC, if sqrt(3)sin C=2 sec A-...

In `triangleABC`, if `sqrt(3)sin C=2 sec A-tan A`, then prove that triangle is right angled.

Text Solution

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We have `sqrt(3)sinC=2 sec A-tan A`
`therefore (sqrt(3)sinC)cos A+sin A=2`.
Now, `(sqrt(3) sinC)cos A+sinA le sqrt((sqrt(3)sinC)^(2)+1)`
`rArr 2 le(3sin^(2)C+1)`
`rArr sin^(2) C ge1`
`rArr sinC=1`
`rArr angle C=(pi)/(2)`
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