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प्रश्न
if `cosec A = sqrt2` find the value of `(2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A))`
उत्तर
Given `cosec A = sqrt2`
We have to find the value of the expression `(2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A))`
We know that
`cosec A =sqrt2`
`=> sin A = 1/(cosec A) = 1/sqrt2`
`cos A = sqrt(1 - sin^2 A) = sqrt(1 - (1/sqrt2)^2) = 1/sqrt2`
`tan A = sin A/cos A = (1/sqrt2)/(1/sqrt2) = 1`
`cot A = 1/tan A = 1/1 = 1`
Therefore,
`(2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A)) = (2 xx (1/sqrt2)^2 + 3 xx 1^2)/(4(1^2 - (1/sqrt2)^2))`
= 2
Hence, the value of the given expression is 2
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