sin bình x + cos bình (4x) = 1

Đáp án và giải thích các bước giải:

`sin^{2}x+cos^{2}4x=1`

`<=>` `cos^{2}4x=1-sin^{2}x`

`<=>` `cos^{2}4x=cos^{2}x`

`<=>` \(\left[ \begin{array}{l}cos4x=cosx \text{ (*)}\\cos4x=-cosx\text{ (**)}\end{array} \right.\) 

`(**)` `<=>` `4x=+-x+2k\pi`

`<=>` \(\left[ \begin{array}{l}x=\dfrac{2k\pi}{3}\\x=\dfrac{2k\pi}{5}\end{array} (k∈\mathbb{Z})\right.\) 

`(**``**)` `<=>` `4x=x-\pi+-2k\pi`

`<=>` \(\left[ \begin{array}{l}x=\dfrac{\pi}{5}+\dfrac{2k\pi}{5}\\x=-\dfrac{\pi}{3}+\dfrac{2k\pi}{3}\end{array} (k∈\mathbb{Z})\right.\)

`->` \(\left[ \begin{array}{l}x=\dfrac{k\pi}{5}\\x=\dfrac{k\pi}{3}\end{array}(k∈\mathbb{Z}) \right.\)