1.

Find the general solution of the equation `5cos^(2)theta+7sin^(2)theta-6=0`.

Answer» Given equation, `5cos^(2)theta+7sin^(2)theta-6=0`
`rArr" "5cos^(2)theta+7(1-cos^(2)theta)-6=0`
`rArr" "5cos^(2)theta+7-7cos^(2)theta-6=0`
`rArr" "5cos ^(2)theta+7-7cos^(2)theta-6=0" "rArr" "-2cos^(2)theta+1=0`
`rArr" "2cos^(2)theta -1=0" "[because cos^(2)theta=cos^(2)alpha thereforetheta=npipmalpha]`
`rArr" "cos^(2)theta=(1)/(2)`
`rArr" "cos^(2)theta=cos^(2)""(pi)/(4)`
`therefore" "theta=npipm(pi)/(4)`


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