1.

For acute angle `theta`, prove the following: (i) `sec^2thetacosecthetage4` (ii) `sec^2theta+cosec^2thetage4`

Answer» Using `A.M.geG.M.`
`(sin^2theta+cos^2thet)/2ge(sin^2thetacos^2theta)^(1//2)`
`rArr 1/2ge(sin^2thetacos^2theta)^(1//2)rArrsin^2thetacos^2thetale1/4`
`=sec^2thetacosec^2thetage4rArr(sin^2theta+cos^2theta)/(sin^2thetacos^2theta)ge4`
`rArr sec^2theta+cosec^2thetage4`


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