\(\Leftrightarrow\cos\left(2x-10^o\right)=\cos120^o\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-10^o=120^o+k360^o\\2x-10^o=180^o-120^o+k360^o\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=130^o+k360^o\\2x=70^o+k360^o\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=65^o+k180^o\\x=35^o+k180^o\end{matrix}\right.\left(k\in Z\right)\)
GPT: \(\sin\left(2x-10^o\right)=-\dfrac{\sqrt{3}}{2}\)
GPT: \(\sin\left(2x-20^o\right)=\dfrac{\sqrt{3}}{2}\)
Giải phương trình sau:
a, \(\sin\left(2x\right)+\sin\left(x\right)-\dfrac{1}{2\sin\left(x\right)}-\dfrac{1}{\sin\left(2x\right)}=2\cot\left(2x\right)\)
b, \(\left(\sin\left(2x\right)+cos\left(2x\right)\right)cos\left(x\right)+2cos\left(2x\right)-sin\left(x\right)=0\)
c, \(\sin\left(2x\right)-\cos\left(2x\right)+3\sin\left(x\right)-\cos\left(x\right)-1=0\)
GPT: \(\sin\left(2x+\dfrac{\pi}{4}\right)=-\dfrac{1}{2}\)
Tìm giá trị max, min của các hàm số sau:
1, y= 2 - \(\sin\left(\dfrac{3\pi}{2}+x\right)\cos\left(\dfrac{\pi}{2}+x\right)\)
2, y= \(\sqrt{5-2\sin^2x.\cos^2x}\)
GPT: \(2\sin\left(2x+\dfrac{\pi}{4}\right)=\sqrt{2}\)
chứng minh đẳng thức lượng giác
a) \(\dfrac{1-cos^2\left(\dfrac{\pi}{2}-x\right)}{1-sin^2\left(\dfrac{\pi}{2}-x\right)}\) - cot\(\left(\dfrac{\pi}{2}-x\right)\) . tan\(\left(\dfrac{\pi}{2}-x\right)\) = \(\dfrac{1}{sin^2x}\)
b) \(\left(\dfrac{1}{cos2x}+1\right)\).tan\(x\) = \(tan2x\)
chứng minh đẳng thức lượng giác
a) \(\dfrac{1-cos^2\left(\dfrac{\pi}{2}-x\right)}{1-sin^2\left(\dfrac{\pi}{2}-x\right)}\)- cot\(\left(\dfrac{\pi}{2}-x\right)\).tan\(\left(\dfrac{\pi}{2}-x\right)\)= \(\dfrac{1}{sin^2x}\)
b) \(\left(\dfrac{1}{cos2x}+1\right)\).tan\(x\) = tan\(2x\)
Giải phương trình:
\(\dfrac{1+sin\left(2x\right)+cos\left(2x\right)}{1+cot^2\left(x\right)}=sin\left(x\right)\left(sin2x+2sin^2x\right)\)
Mk cảm ơn trc ạ
