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Question
If `sin theta = x , " write the value of cot "theta .`
Solution
`cot theta = cos theta / sin theta `
=` sqrt(1-sin^2 theta)/sin theta`
=`sqrt(1-x^2)/2`
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We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
