1.

Solve the inequation `2^(1/(cos^2 x))sqrt(y^2-y+1/2)

Answer» `2^(1/cos^(2)x) sqrt(y^(2)-y+1//2) le1`…………(i)
`2^(1/(cosp^(2)x)) sqrt((y-1/2)^(2)+(1/2)^(2)) le1`
Miniumum value of `2^((1)/(cos^(2)x)=2`
Minimum value of `sqrt((y-1/2)^(2)+(1/2)^(2))=1/2`
`rArr` Minimum value of `2^(1/(cos^(2)x)) sqrt(y^(2)-y+1/2)` is 1
`rArr` (i) is possible when `2^(1/(cos^(2)x)) sqrt((y-1/2)^(2)+(1/2)^(2))=1`
`rArr cos^(2)x=1` and `y=1/2 rArr cosx = +1 rArr x=npi`, where `n in I`,
Hence, `x=npi, n in I` and `y=1//2`.


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