1.

Find the general solution of each of the equations : (i) `4sin^(2)x=1` (ii) `2 cos^(2)x=1` (iii) `cot^(2)x=3`

Answer» (i) `4sin^(2)x=1rArrsin^(2)x=(1)/(4)=((1)/(2))^(2)="sin"^(2)(pi)/(6)`
`rArrsin^(2)x="sin"^(2)(pi)/(6)`
`rArrx={npi+-(pi)/(6)}` , where `ninI`
Hence , the general solution is x = `(npi+-(pi)/(6))`, `n inI`.
(ii) `2cos^(2)x=1rArrcos^(2)x=(1)/(2)=((1)/(sqrt(2)))^(2)="cos"^(2)(pi)/(4)`
`rArr cos ^(2)x="cos"^(2)(pi)/(4)`
`rArrx=(npi+-(pi)/(4))`, where `ninI`.
Hence , the general solution is x = `(npi+-(pi)/(4)),ninI`.
(iii) `cot^(2)x=3rArrtan^(2)x=(1)/(3)=((1)/(sqrt(3)))^(2)="tan"^(2)(pi)/(6)`
`rArrtan^(2)x=" tan "^(2)(pi)/(6)`
`rArrx=(npi+-(pi)/(6))`, where `ninI`.
Hence , the general solution is `(npi+-(pi)/(6))`, where `ninI`.


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