Question

Cos3xCos³x +Sin3xSin³x=0​

Answer 1

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Answer 2

Answer: x=pi/4+(pi/2)×k

Step-by-step explanation: cos(3x)cos^3(x)+sin(3x)sin^3(x)=0

(4cos^3(x)-3cos(x))cos^3(x)+(-sin^3(x)+3sin(x))sin^3(x)=0

4cos^6(x)-3cos^4(x)-4sin^6(x)+3sin^4(x)=0

4(cos^6(x)-sin^6(x))+3(sin^4(x)-cos^4(x))=0

4(cos^3(x)-sin^3(x))(cos^3(x)+sin^3(x))+3(sin^2(x)-cos^2(x))(sin^2(x)+cos^2(x))=0

4(cos^2(x)-sin^2(x))(1-cos^2(x)sin^2(x))-3cos(2x)=0

4cos(2x)(1-(1/4)sin^2(2x))-3cos(2x)=0

cos(2x)(4-sin^2(2x)-3)=0

cos(2x)(1-sin^2(2x))=0

cos^3(2x)=0

2x=pi/2+pi×k

x=pi/4+(pi/2)×k