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The most general solution of 2^(sin x)+2...

The most general solution of `2^(sin x)+2^(cos x)=2^(1-(1)/(sqrt(2)))` is `(n in Z)`

Text Solution

Verified by Experts

The correct Answer is:
`x=2n pi+(3pi)/(4),2n pi+(pi)/(12),n in Z`
`3^(((1)/(2)+log_(3)(cos x + sin x)))-2^(log_(2)(cos x - sin x)=sqrt(2))`
or `sqrt(3)(cos x + sin x) - (cos x - sin x) = sqrt(2)`
or `sqrt(3) cos x + sqrt(3) sin x - cos x + sin x = sqrt(2)`
or `(sqrt(3)+1)sin x + (sqrt(3)-1)cos x = (2sqrt(2))/(2)/(2)`
or `((sqrt(3)+1)/(2sqrt(2)))sin x + ((sqrt(3)-1)/(2sqrt(2)))cos x = (1)/(2)`
or `sin (x + (5pi)/(12))=(1)/(2)`
or `x + (5pi)/(12)=2n pi pm (pi)/(3), n in Z`
or `x = 2n pi pm(pi)/(3)-(5pi)/(12)`
or `x = 2n pi +(3pi)/(4), 2n pi + (pi)/(12), n in Z`
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