Solving for x: (sin x)^6 + (cos x)^6 = 5/6 ((sin x)^4 + (cos x)^4)

[no name]

hey ...


find (x) ...
(sin x )^6 + (cos x) ^6 = 5/6 ( (sin x)^4 + (cos x)^4)

cheers

 

[Padford]

x= 22.5
.. I think

 

[dextercioby]

There's the same problem posted in the "Brain Teasers" Section where I've given the correct answers...

Daniel.

 

[HallsofIvy]

x= 22.5
.. I think

If a problem involving trig functions does not specifically involve angle measured in degrees, x must be in "radians".

x= pi/8 is correct.

 

[Pseudo Statistic]

How do you solve such a problem? (Involving both functions)

 

[dextercioby]

Use that:$$\sin^{2}x=1-\cos^{2}x$$ and the fact that the powers in the equation are even...

Daniel.

 

[Zurtex]

Erm, I think if you play around with it a bit you should be able to reduce it to :

$$\cos 4x = 0$$