4sin^4x + cos^4x=1

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

4sin^4x + cos^4x=1

Postby Guest » Sun Oct 07, 2018 12:19 pm

Solve the trigonometric equation:
[tex]4sin^4x + cos^4x=1[/tex]
Guest
 

Re: 4sin^4x + cos^4x=1

Postby Guest » Mon Oct 08, 2018 1:40 am

Do you know the answers ?
Guest
 

Re: 4sin^4x + cos^4x=1

Postby Guest » Mon Oct 08, 2018 4:18 pm

[tex]4sin^4x+cos^4x=1\Rightarrow(2sin^2x+cos^2x)^2-4sin^2xcos^2x=1\Rightarrow(1+sin^2x)^2-4sin^2xcos^2x=1\Rightarrow2sin^2x+sin^4x-4sin^2x(1-sin^2x)=0[/tex]

[tex]sin^2x(2+sin^2x-4+4sin^2x)=0\Rightarrow sinx=0\cup sin^2x=\frac{2}{5}\Rightarrow x=k\pi\cup x=\pm arcsin\frac{\sqrt{10}}{5}+l\pi[/tex]
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