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Match the following lists: |
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Answer» `=cos (|cosx|-|-SINX|)` `=cos(|cosx|-|sinx|)` `=cos(|sin x|-|cosx|)` `=f(x)` b. `f(x+pi//2)=cos[tan(x+pi//2)+cot(x+pi//2)].` `cos[tan(x+pi//2)-cot(x+pi//2)]` `=cos[-cotx-tanx]*cos[-cotx+tanx]` `=cos(tanx+cotx)*cos(tanx-cotx)` `=f(x)` c. The period of `sin^(-1)(sinx) " is " 2pi.` The period of `e^(tanx) " is " pi`. Thus, the period of `f(x)" is " LCM (2pi,pi)=2pi.` d. The given function is `f(x)=sin^(3)x sin 3x` `=((3sinx-sin 3x)/(4)) sin 3x` `=(3)/(8) (cos 2x-cos 4x)-(1)/(8)(1-cos6x)` Thus, the period of `f(x) " is " pi.` |
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