1.

If x ne (npi)/2, n in I and (cosx)^(sin^(2)x-3sinx+2)=1, then find the general solutions of x.

Answer»

SOLUTION :As `x ne (npi)/2 rArr COSX ne 0,1,-1`
So, `(cosx)^(sin^(2)x-3sinx+2) = 1 rArr sin^(2)x-3sinx+2=0`
`therefore (sinx-2)(sinx-1)=0 rArr sinx=1,2`
Where `sinx=2` is not POSSIBLE and `sinx=2` is not possible and `sinx=1` which is also not possible as `x ne (npi)/(2)`
`therefore` no general solutions is possible. Ans.


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