Bài 1: a) Đk: $\sin x\ne0\Leftrightarrow x\ne k\pi(k\in\mathbb Z)$ TXĐ: $D=\mathbb R\backslash\{k\pi,k\in\mathbb Z\}$ b) Đk: $\left\{ \begin{array}{l} \cos x\ne0 \\ 1-\cos x\ne0 \end{array} \right .$ $\Leftrightarrow \left\{ \begin{array}{l} x\ne \dfrac{\pi}{2}+k\pi(k\in\mathbb Z) \\ \cos x\ne1\Leftrightarrow x\ne k2\pi(k\in\mathbb Z) \end{array} \right .$ TXĐ: $D=\mathbb R\backslash\{ \dfrac{\pi}{2}+k\pi;k2\pi,k\in\mathbb Z\}$ c) Đk: $\cos\left({x-\dfrac{\pi}{6}}\right)\ne0$ $\Rightarrow x-\dfrac{\pi}{6}\ne\dfrac{\pi}{2}+k\pi$ $\Rightarrow x\ne\dfrac{2\pi}{3}+k\pi,k\in\mathbb Z$ TXĐ: $D=\mathbb R\backslash\{\dfrac{2\pi}{3}+k\pi,k\in\mathbb Z\}$ d) Đk: $\cos \left({x-\dfrac{2\pi}{3}}\right)\ne0$ $\Leftrightarrow x-\dfrac{2\pi}{3}\ne\dfrac{\pi}{2}+k\pi$ $\Leftrightarrow x\ne\dfrac{7\pi}{6}+k\pi,k\in\mathbb Z$ Bài 2: a) $\cos 2x=\dfrac{\sqrt3}{2}=\cos\dfrac{\pi}{6}$ $\Rightarrow 2x=\pm\dfrac{\pi}{6}+k2\pi$ $\Rightarrow x=\pm\dfrac{\pi}{12}+k\pi,k\in\mathbb Z$ b) $\sin (x+80^o)=\dfrac{\sqrt2}{2}=\sin 45^o$ $\Rightarrow \left[\begin{array}{l} x+80^o=45^o+k360^o \\ x+80^o=180^o-45^o+k360^o \end{array} \right .$ $\Rightarrow \left[\begin{array}{l} x=-5^o+k360^o \\ x=55^o+k360^o \end{array} \right .(k\in\mathbb Z)$ c) $\sin x=\dfrac{1}{2}$ $\Rightarrow \left[\begin{array}{l} x=\dfrac{\pi}{6}+k2\pi \\ x=\dfrac{5\pi}{6}+k2\pi\end{array} \right .(k\in\mathbb Z)$ d) $\sin x=\sin 80^o$ $\Rightarrow \left[\begin{array}{l} x=80^o+k360^o \\ x=100^o+k360^o \end{array} \right .(k\in\mathbb Z)$ e) ${\tan}^2x-6\tan x+5=0$ Đk: $\cos x\ne0\Leftrightarrow x\ne\dfrac{\pi}{2}+k\pi,k\in\mathbb Z$ $\Rightarrow \left[\begin{array}{l} \tan x=5\\ \tan x=1\end{array} \right .$ $\Rightarrow \left[\begin{array}{l} x=\arctan 5+k\pi(tm) \\ x=\dfrac{\pi}{4}+k\pi(tm)\end{array} \right .(k\in\mathbb Z)$ f) $\sin x+\cos x=1$ $\Rightarrow \dfrac{1}{\sqrt2}\sin x+\dfrac{1}{\sqrt2}\cos x=\dfrac{1}{\sqrt2}$ $\Rightarrow \sin(x+\dfrac{\pi}{3})=\dfrac{1}{sqrt2}$ $\Rightarrow \left[\begin{array}{l} x+\dfrac{\pi}{3}=\dfrac{\pi}{4}+k2\pi\\ x+\dfrac{\pi}{3}=\dfrac{3\pi}{4}+k2\pi\end{array} \right .$ $\Rightarrow \left[\begin{array}{l} x=-\dfrac{\pi}{12}+k2\pi\\ x=\dfrac{5\pi}{12}+k2\pi\end{array} \right .(k\in\mathbb Z)$ g) $\sqrt3\sin x+\cos x=2$ $\Rightarrow \dfrac{\sqrt3}{2}\sin x+\dfrac{1}{2}\cos x=1$ $\Rightarrow \sin(x+\dfrac{\pi}{6})=1$ $\Rightarrow x+\dfrac{\pi}{6}=\dfrac{\pi}{2}+k2\pi,k\in\mathbb Z$

a. Cos2x = √3/2

<=> cos2x = cosπ/6

<=> 2x= +-π/6 + k2π

<=> x = +-π/12 + k2π (k thuộc Z)

b. Sin(x+80°) =√2/2

<=> sin(x+80°) = sin45°

<=> x+80°= 45°+ 360°k hoặc x+ 80° =180°-45°+360°k

<=> (tự tính nhé)

c,d (tương tự vậy)

g. √3sinx + cosx =2

<=> √3/2.sinx + 1/2.cosx =1

<=> cosπ/6.sinx+ sinπ/6.cosx=1

<=> sin(π/6 + x) =1

<=> π/6 + x = π/2+k2π

<=> ( tự tính kkk)