The range `f(x)=cos2x-sin2x` contains the setA. [2, 4]B. `[-1, 1]`C. ` – InterviewSolution

InterviewSolution

1.	The range `f(x)=cos2x-sin2x` contains the setA. [2, 4]B. `[-1, 1]`C. `[-sqrt(2), sqrt(2)]`D. `(-sqrt(2),2)`
Answer» Correct Answer - C Let f(x)=cos2x-sin2x `f(x)=(1)/(sqrt(2))[sqrt(2)cos2x-sin2x]` `f(x)=sqrt(2)[(1)/(sqrt(2))cos2x-(1)/(sqrt(2))sin2x]` `f(x)=sqrt(2)[cos.(pi)/(4)cos2x-sin.(pi)/(4)sin2x]` `f(x)=sqrt(2)[cos((pi)/(4)+2x)]` We know, `-1lecos((pi)/(4)+2x)le1` `implies-sqrt(2)lesqrt(2)cos((pi)/(4)+2x)lesqrt(2)` `implies-sqrt(2)lef(x)lesqrt(2)` `therefore " Range of "f(x)=[-sqrt(2),sqrt(2)]`

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