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Trig Identity and Pythagorean

  • Thread starter nzashadow
  • Start date
  • #1
10
0

Homework Statement



3(sin(x)^4+cos(x)^4)-2(sin(x)^6+cos(x)^6)=1

(these are sinx raised to the 4 and 6 powers, not x^4or6)

Homework Equations



Pythagorean Identities

The Attempt at a Solution



I've tried using pythagorean identities to change everything to terms of sine or cosine. I've been hoping to manipulate it enough to get enough cos(x)^2+sin(x)^2 to try and turn all trig functions into a numerical value. Maybe this is right and I'm missing something on the way or not going far enough. I have figured out that the 3 and the 2 are necessary to equal 1, and other values such as 2 and 1 respectively will not equate to 1, therefore (sin(x)^4+cos(x)^4)-(sin(x)^6+cos(x)^6) =/= 1-1 (although I am not sure if this is relevant.)

If anyone can give me a hint at how to correctly approach the problem that would be nice, I don't want anyone to actually work the problem out for me. Thank you
 

Answers and Replies

  • #2
Avodyne
Science Advisor
1,396
87
Try setting [itex]y=(\sin x)^2[/itex], and writing everything in terms of [itex]y[/itex].
 
  • #3
108
0
I rewrote it as 3((sin2)2+cos4)-2(sin2*sin4+cos6)

And then using sin2=1-cos2, and some FOILing, the messy algebra worked out nicely.
 
  • #4
10
0
Thanks guys, got it.
 

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