If Cot Theta = Sqrt3 Find the Value of (Cosec^2 Theta + Cot^2 Theta)/(Cosec^2 Theta - Sec^2 Theta) - Mathematics

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if `cot theta = sqrt3` find the value of `(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)`

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Solution

`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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Chapter 11: Trigonometric Identities - Exercise 11.2 [Page 54]

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RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.2 | Q 8 | Page 54

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