1.

The period of the function`f(x)=c^((sin^2x) +sin^2 (x+pi/3)+cosxcos(x+pi/3))`is (where `c`is constant)A. 1B. `(pi)/(2)`C. `pi`D. None of these

Answer» Correct Answer - D
`sin^(2)x+sin^(2)(x+(pi)/(3))+cosxcos(x+(pi)/(3))`
`=sin^(2)x+((sinx)/(2)+(sqrt(3)cosx)/(2))^(2)+cosx((sinx)/(2)-(sqrt(3)cosx)/(2))`
`=sin^(2)x+(sin^(2)x)/(4)+(3cos^(2)x)/(4)+(cos^(2)x)/(2)`
`=(5sin^(2)x)/(4)+(5cos^(2)x)/(4)`
`=(5)/(4)`
Hence, `f(x)=c^(5//4)=` constant, which is periodic but has no fixed period.


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