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If ` tan theta =(1)/(sqrt(5)), " write the value of " (("cosec"^(2)theta-sec^(2)theta))/(("cosec"^(2)theta+sec^(2)theta)).`

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If ` tan theta =(1)/(sqrt(5)), " write the value of " (("cosec"^(2)theta-sec^(2)theta))/(("cosec"^(2)theta+sec^(2)theta)).`
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Correct Answer - `(2)/(3)`
`"cosec"^(2)theta=(1+cot^(2)theta)=(1+5)=6, sec^(2)theta=(1+tan^(2)theta)=(1+(1)/(5))=(6)/(5).`
`therefore (("cosec"^(2)theta-sec^(2)theta))/(("cosec"^(2)theta+sec^(2)theta))=((6-(6)/(5)))/((6+(6)/(5)))=(24)/(36)=(2)/(3).`
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