a: ĐKXĐ: \(2x-40^0\ne90^0+k\cdot180^0\)
=>\(x\ne65^0+k\cdot90^0\)
\(tan\left(2x-40^0\right)=tan\left(-100^0\right)\)
=>\(2x-40^0=-100^0+k\cdot180^0\)
=>\(2x=-60^0+k\cdot180^0\)
=>\(x=-30^0+k\cdot90^0\left(nhận\right)\)
b: ĐKXĐ: \(\dfrac{x}{2}\ne k\Omega\)
=>\(x\ne k2\Omega\)
\(\sqrt{3}\cdot cot\left(\dfrac{x}{2}\right)=-3\)
=>\(cot\left(\dfrac{x}{2}\right)=-\sqrt{3}\)
=>\(\dfrac{x}{2}=-\dfrac{\Omega}{6}+k\Omega\)
=>\(x=-\dfrac{\Omega}{3}+k2\Omega\)(nhận)
c: \(sin\left(2x+15^0\right)+cos\left(2x-15^0\right)=0\)
=>\(cos\left(2x-15^0\right)=-sin\left(2x+15^0\right)=sin\left(-2x-15^0\right)\)
=>\(cos\left(2x-15^0\right)=cos\left(90^0+2x+15^0\right)=cos\left(2x+105^0\right)\)
=>\(\left[{}\begin{matrix}2x-15^0=2x+105^0+k\cdot360^0\\2x-15^0=-2x-105^0+k\cdot360^0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}0x=120^0+k\cdot360^0\left(loại\right)\\4x=-90^0+k\cdot360^0\end{matrix}\right.\)
=>\(x=-22,5^0+k\cdot90^0\)
d: ĐKXĐ: \(3x\ne\dfrac{\Omega}{2}+k\Omega\)
=>\(x\ne\dfrac{\Omega}{6}+\dfrac{k\Omega}{3}\)
\(tan3x=\dfrac{2025}{2024}\)
=>\(3x=arctan\left(\dfrac{2025}{2024}\right)+k\Omega\)
=>\(x=\dfrac{1}{3}\cdot arctan\left(\dfrac{2025}{2024}\right)+\dfrac{k\Omega}{3}\)(nhận)
e: \(\left(2+cosx\right)\left(4\cdot sinx-3\right)=0\)
mà \(1< =cosx+2< =3\)
nên \(4\cdot sinx-3=0\)
=>\(sinx=\dfrac{3}{4}\)
=>\(\left[{}\begin{matrix}x=arcsin\left(\dfrac{3}{4}\right)+k2\Omega\\x=\Omega-arcsin\left(\dfrac{3}{4}\right)+k2\Omega\end{matrix}\right.\)
f:
ĐKXĐ: \(\left\{{}\begin{matrix}2x\ne\dfrac{\Omega}{2}+k\Omega\\x\ne k\Omega\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\Omega}{4}+\dfrac{k\Omega}{2}\\x\ne k\Omega\end{matrix}\right.\)
\(tan2x\cdot cotx=1\)
=>\(tan2x=\dfrac{1}{cotx}\)
=>\(tan2x=tanx\)
=>\(2x=x+k\Omega\)
=>\(x=k\Omega\)(loại)
