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If `tan theta=(20)/(21), ` show that `(("cosec"^(2)theta -sec^(2) theta))/(("cosec"^(2)theta+cos ^(2)theta ))=(3)/(4).`

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If `tan theta=(20)/(21), ` show that `(("cosec"^(2)theta -sec^(2) theta))/(("cosec"^(2)theta+cos ^(2)theta ))=(3)/(4).`
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`tan theta =(1)/(7)= (BC)/(AB).`
`therefore AC^(2)=AB^(2)+BC^(2)=(sqrt(7))^(2)+(1)^(2)=(7+1)=8impliesAC=sqrt(8)=2sqrt(2).`
` therefore "cosec" theta=(AC)/(AB)=(2sqrt(2))/(sqrt(7))implies sec^(2)theta theta =(8)/(7).`
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