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प्रश्न
if `cot theta = sqrt3` find the value of `(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)`
उत्तर
`Given `cot theta = sqrt3`
We have to find the value of the expression `(cosec^2 theta = cot^2 theta)/(cosec^2 theta - sec^2 theta)`
We know that
`cot theta = sqrt3 => cot^2 theta = 3`
`cosec^2 theta =1 + cot^2 theta = 1 + (sqrt3)^2 = 4`
`sec^2 theta = 1/cos^2 theta = 1/(1 - sin^2 theta) = 1/(1 - 1/cosec^2 theta) = 1/(1 - 1/4) = 4/3`
Therefore
`(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta) = (4 + 3)/(4 - 4/3)`
`= 21/8`
Hence, the value of the given expression is 21/8
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