Đáp án:
\(\cos a=\dfrac{1}{2}\)
\(\sin a=\pm \dfrac{\sqrt{3}}{2}\)
\(\tan a=\pm \sqrt{3}\)
\(\cot a=\pm \dfrac{\sqrt{3}}{3}\)
Giải thích các bước giải:
\(4.\sin^{2} a=4\cos a +1\)
\(\Leftrightarrow 4(1-\cos^{2} a)=4\cos a+1\)
\(\Leftrightarrow 4\cos^{2} a+4\cos a-3=0\)
Đặt \(t=\cos a\) \((t \epsilon [-1;1])\)
\(4t^{2}+4t-3=0\)
\(\Leftrightarrow \) \(\left[ \begin{array}{l}t=\dfrac{1}{2} \text{(nhận)}\\t=-\dfrac{3}{2} \text{(loại)}\end{array} \right.\)
\(\Rightarrow \cos a=\dfrac{1}{2}\)
\(\sin^{2} a+\cos^{2} a=1\)
\(\Leftrightarrow \sin a=\sqrt{1-(\dfrac{1}{2})^{2}}=\pm \dfrac{\sqrt{3}}{2}\)
\(\tan a=\dfrac{\sin a}{\cos a}=\dfrac{\pm \dfrac{\sqrt{3}}{2}}{\dfrac{1}{2}}=\pm \sqrt{3}\)
\(\cot a=\dfrac{1}{\tan a}=\dfrac{1}{\pm \sqrt{3}}=\pm \dfrac{\sqrt{3}}{3}\)
