Question

Giải Phương Trình sau?
Tan2x = Cot(x +pi/4)

Answer 1

tan2x = cot\(\left(x+\dfrac{\pi}{4}\right)\)

<=>\(\dfrac{1}{cot2x}\)=\(\cot\left(x+\dfrac{\pi}{4}\right)\)

<=>1= \(\cot\left(x+\dfrac{\pi}{4}\right)\) . cot2x

<=>1=\(\dfrac{cos\left(x+\dfrac{\pi}{4}\right)}{sin\left(x+\dfrac{\pi}{4}\right)}\) . \(\dfrac{cos2x}{sin2x}\)

<=>1=\(\dfrac{\dfrac{1}{2}\left[cos\left(x+\dfrac{\pi}{4}-2x\right)+cos\left(x+\dfrac{\pi}{4}+2x\right)\right]}{\dfrac{1}{2}\left[cos\left(x+\dfrac{\pi}{4}-2x\right)-cos\left(x+\dfrac{\pi}{4}+2x\right)\right]}\)

<=>1=\(\dfrac{cos\left(\dfrac{\pi}{4}-x\right)+cos\left(3x+\dfrac{\pi}{4}\right)}{cos\left(\dfrac{\pi}{4}-x\right)-cos\left(3x+\dfrac{\pi}{4}\right)}\)

r b quy đồng x giải pt là ra