1.

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

Answer»

Solution :`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)thetatheta =(8)/(7).`


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