a/\(\sin3x+\cos2x=1+2\sin x\cos2x\)
b/\(\sin^3x+\cos^3x=2\left(\sin^5x+\cos^5x\right)\)
c/\(\dfrac{\tan x}{\sin x}-\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{2}}{2}\)
d/\(\dfrac{\cos x\left(\cos x+2\sin x\right)+3\sin x\left(\sin x+\sqrt{2}\right)}{\sin2x-1}=1\)
e/\(\sin^2x+\sin^23x-2\cos^22x=0\)
f/\(\dfrac{\tan x-\sin x}{\sin^3x}=\dfrac{1}{\cos x}\)
g/\(\sin2x\left(\cos x+\tan2x\right)=4\cos^2x\)
h/\(\sin^2x+\sin^23x=\cos^2x+\cos^23x\)
k/\(4\sin2x=\dfrac{\cos^2x-\sin^2x}{\cos^6x+\sin^6x}\)
mọi người giải giúp em với em đang cần gấp ạ
1. CM:
\(\dfrac{1}{2}\le\dfrac{\sin x+2\cos x+3}{2\sin x\cos x+3}\le2\)
2. Giải PT:
a) \(\dfrac{1}{\cos x}=4\sin x+6\cos x\)
b) \(\sin^3\left(x-\dfrac{\pi}{4}\right)=\sqrt{2}\sin x\)
c) \(\dfrac{1}{\cos x}+\dfrac{1}{\sin2x}=\dfrac{2}{\sin4x}\)
Tìm GTLN, GTNN:
a, \(y=\sin x+\cos x\).
b, \(y=\dfrac{1}{2}\sin x+\dfrac{\sqrt{3}}{2}\cos x+3\).
c, \(y=\sqrt{3}\sin2x-\cos2x\).
Giải PT
a1) \(3.\cos4x-2^{ }\cos^23x=1\)
a2) \(2\cos2x-8\cos x+7=\dfrac{1}{\cos x}\)
a3) \(\dfrac{\left(1+\sin x+\cos2x\right)\sin\left(x+\dfrac{\pi}{4}\right)}{1+\tan x}=\dfrac{1}{\sqrt{2}}\cos x\)
a4) \(9\sin x+6\cos x-3\sin2x+\cos2x=8\)
Tìm TXĐ:
a, \(y=\dfrac{1}{2}\sin\left(2x-1\right)-\cos\left(x^2-2\right)\).
b, \(y=\sin\sqrt{2x-4}\).
c, \(y=\sqrt{1-\cos^2x}\).
1) sin\(\sin\left[\pi sin2x\right]\)=1
2) cos\(\left[\dfrac{\pi}{2}.cos\left(x-\dfrac{\pi}{4}\right)\right]\)=\(\dfrac{\sqrt{2}}{2}\)
3) sin(x+24*) + sin(x+144*) = cos20*
1. Tìm m để PT có nghiệm:
a) \(\sqrt{3}\cos^2x+\dfrac{1}{2}\sin2x=m\)
b) \(3\sin^2x-2\sin x\cos x+m=0\)
c) \(\sin^2x+2\left(m-1\right)\sin x\cos x-\left(m+1\right)\cos^2x=m\)
1. Tìm m để PT có nghiệm:
a) \(\sqrt{3}\cos^2x+\dfrac{1}{2}\sin2x=m\)
b) \(3\sin^2x-2\sin x\cos x+m=0\)
c) \(^{ }\sin^2x+2\left(m-1\right)\sin x\cos x-\left(m+1\right)\cos^2x=m\)
Cho \(\dfrac{1}{tan^2a}+\dfrac{1}{cot^2a}+\dfrac{1}{sin^2a}+\dfrac{1}{cos^2a}=7\).
Tính cos4a
