Advanced Placement (AP)
Schweigart938
2018-06-26 22:45:12
[Pre-Calc] Verify the following equations: [latex]1) sin(3x) = 3sin(x)-4sin^3x \\\ 2) cos(3x)=4cos^3x-3cosx [/latex] Please show your work and start using the left side of the equation.
ANSWERS
TrinidadMortell839
2018-06-27 01:38:00

3sin(x)3⁢sinx and −4sin3(x)-4⁢sin3x. sin(3x)=−4sin3(x)+3sin(x)sin3⁢x=-4⁢sin3x+3⁢sinxApply the sine triple-angle identity. sin(3x)=sin(3x)sin3⁢x=sin3⁢xFor the two functions to be equal, the arguments of each must be equal. 3x=3x3⁢x=3⁢xMove all terms containing xx to the left side of the equation. Since 3x3⁢x contains the variable to solve for, move it to the left side of the equation by subtracting 3x3⁢x from both sides.3x−3x=03⁢x-3⁢x=0Subtract 3x3⁢x from 3x3⁢x to get 0 Since 0=00=0, the equation will always be true for any value of x

Morge649
2018-06-27 01:39:15

sin(α+β)=sinαcosβ+cosαsinβ,and the double angle formula of cosine:cos(2α)=cos2α−sin2α=2cos2α−1=1−2sin2αthen:sin(3x)=sin(2x+x)=sin(2x)cosx+cos(2x)sinx==(2sinxcosx)⋅cosx+(1−2sin2x)sinx==2sinxcos2x+sinx−2sin3x==2sinx(1−sin2x)+sinx−2sin3x==2sinx−2sin3x+sinx−2sin3x==3sinx−4sin3x.

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