Sin^4 x + cos^4 x = cos4x

Question

Sin^4 x + cos^4 x = cos4x

Answer 1

(1-cos2x)²/4+(1+cos2x)²/4=cos4x
2+2cos²2x=4cos4x
2+2cos²2x=8cos²2x-4
8cos²2x-2cos2x-6=0
4cos²2x-cos2x-3=0
cos2x=a
4a²-a-3=0
D=1+48=49
a1=(1-7)/8=-3/4⇒cos2x=-3/4⇒x=+-1/2arccos3/4+2πn
a2=(1+7)/8=1⇒cos2x=1⇒x=πn

Comments

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