Find the minimum value of the expression \(\displaystyle{y}={\frac{{{16}-{8}{{\sin}^{{2}}{2}}{x}+{8}{{\cos}^{{4}}{x}}}}{{{{\sin}^{{2}}{2}}{x}}}}\)

Willie Kelley

Willie Kelley

Answered question

2022-04-14

Find the minimum value of the expression
y=168sin22x+8cos4xsin22x

Answer & Explanation

uvredio0of6

uvredio0of6

Beginner2022-04-15Added 17 answers

8cot4x=8(1+cos(2x)2)2
=8(1+2cos(2x)+cos2(2x)4)
=2+4cos(2x)+2cos2(2x)
=2+4t+2t2
t=cos(2x)y
=168(1t2)+2+4t+2t21t2
=10+10t2+4t1t2
=f(t), 1t1

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