Giải các phương trình :
a) \(\cos^2x+\cos^22x-\cos^23x-\cos^24x=0\)
b) \(\cos4x\cos\left(\pi+2x\right)-\sin2x\cos\left(\dfrac{\pi}{2}-4x\right)=\dfrac{\sqrt{2}}{2}\sin4x\)
c) \(\tan\left(120^0+3x\right)-\tan\left(140^0-x\right)=2\sin\left(80^0+2x\right)\)
d) \(\tan^2\dfrac{x}{2}+\sin^2\dfrac{x}{2}\tan\dfrac{x}{2}+\cos^2\dfrac{x}{2}+\cot^2\dfrac{x}{2}+\sin x=4\)
e) \(\dfrac{\sin2t+2\cos^2t-1}{\cot t-\cot3t+\sin3t-\sin t}=\cos t\)
Giai pt
\(5sinx-2=3\left(1-sinx\right)tan^2x\)
\(2.cos2x.cosx=1+cos2x+cos3x\)
\(cos2x+cosx=4sin^2\left(\dfrac{x}{2}\right)-1\)
Giai pt
\(5sinx-2=3\left(1-sinx\right)tan^2x\)
\(2.cos2x.cosx=1+cos2x+cos3x\)
\(cos2x+cosx+4sin^2\left(\dfrac{x}{2}\right)-1\)
Giải pt :
\(tan.\left(x+\dfrac{\pi}{4}\right)+cot\cdot\left(2x-\dfrac{\pi}{3}\right)=0\)
Giải các phương trình :
a) \(\cos\left(22^0-t\right)\cos\left(82^0-t\right)+\cos\left(112^0-t\right)\cos\left(172^0-t\right)=\dfrac{1}{2}\left(\sin t+\cos t\right)\)
b) \(\sin^2\left(t+45^0\right)-\sin^2\left(t-30^0\right)-\sin15^0\cos\left(2t+15^0\right)=\dfrac{1}{2}\sin6t\)
c) \(\sin^82x+\cos^82x=\dfrac{41}{128}\)
d) \(\sqrt{4\cos^2+1}+\sqrt{4\sin^2x+3}=4\)
e) \(\tan\left(\pi\cot t\right)=\cot\left(\pi\sin t\right)\)
Giải: \(\left(cos2x-cos4x\right)^2=6+2sin3x\)
Tính đạo hàm của các hàm số sau :
a) \(y=\dfrac{1+x-x^2}{1-x+x^2}\)
b) \(y=\dfrac{\left(2-x^2\right)\left(3-x^3\right)}{\left(1-x\right)^2}\)
c) \(y=\cos2x-2\sin x\)
d) \(y=\dfrac{\cos x}{2\sin^2x}\)
e) \(y=\cos^2\dfrac{x}{3}\tan\dfrac{x}{2}\)
f) \(y=\sqrt{\sin\left(2x-\dfrac{\pi}{6}\right)}\)
g) \(y=\cos\dfrac{x}{x+1}\)
h) \(y=\dfrac{x^2-1}{\sin3x}\)
i) \(y=3\sin^2x\cos x+\cos^2x\)
k) \(y=\sqrt{7-4x}\cot3x\)
Giải pt
\(2sin\left(x+\dfrac{\pi}{6}\right)+sinx+2cosx=3\)
\(\left(sin2x+cos2x\right)cosx+2cos2x-sinx=0\)
\(sin2x-cos2x+3sinx-cosx-1=0\)
Giai Pt
\(\left(2sinx-cosx\right)\left(1+cosx\right)=sin^2x\)
\(3sin^2x+7cos2x-3=0\)
\(\dfrac{4sin^2x+6sin^2x-9-3cos2x}{cosx}=0\)
