If \cos^6 (x) + \sin^4 (x)=1 find x if x

ardeinduie

ardeinduie

Answered question

2022-01-29

If cos6(x)+sin4(x)=1 find x if x[0,π2]
My attempt:
cos6(x)+sin4(x)=1
cos6(x)+(1cos2(x))2=1
cos6(x)+12cos2(x)+cos4(x)=1
cos6(x)+cos4(x)2cos2(x)=0

Answer & Explanation

ul2ph3ojc

ul2ph3ojc

Beginner2022-01-30Added 12 answers

Hint If we rewrite u=cos2x and factor, the equation becomes
(u+2)u(u1)=0
Alternative hint We have cos6xcos2x and sin4xsin2x nd in both cases equality holds (for x[0,π2]) only for x=0,π2
KickAntitte06

KickAntitte06

Beginner2022-01-31Added 11 answers

Hint:
Clearly, sinx=0cos2x=?
cosx=0sin2x=? are solutions
For 0<a<1
a6<a4<a2

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