\(sin\left(a-\frac{\pi}{4}\right)cos\left(\frac{\pi}{3}-a\right)-cos\left(a-\frac{\pi}{4}\right)sin\left(\frac{\pi}{3}-a\right)\)
\(=sin\left(a-\frac{\pi}{4}-\left(\frac{\pi}{3}-a\right)\right)=sin\left(a-\frac{\pi}{4}-\frac{\pi}{3}+a\right)\)
\(=sin\left(2a-\frac{7\pi}{12}\right)\)
Rút gọn biểu thức :
A = sin(a - \(\frac{\pi}{4}\))cos(\(\frac{\pi}{3}\) - a) - cos(\(\frac{\pi}{4}\) - a)sin(\(\frac{\pi}{3}\) - a)
bài 1: a) \(sin\left(2x+\dfrac{\pi}{6}\right)+sin\left(x-\dfrac{\pi}{3}\right)=0\)
b) \(sin\left(2x-\dfrac{\pi}{3}\right)-cos\left(x+\dfrac{\pi}{3}\right)=0\)
c) \(sin\left(2x+\dfrac{\pi}{3}\right)+cos\left(x-\dfrac{\pi}{6}\right)=0\)
1)giải pt a)√2 cos2x-1=0
b) sinx =cos3x
c) cos (x+π/3) +sin(3x+π/4)=0
d)tan 2x = cot (x+π/4)
e) sin x = √3 cos x
f) tan^2(π/3-2x)-3=0
cos^4x+sin^x+cos(x-pi/4)sin(3x-pi/4)-3/2=0
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*
Giải phương trình \(cos^4x+\sin^4x+cos\left(x-\frac{\pi}{4}\right)\times sin\left(3x-\frac{\pi}{4}\right)-\frac{3}{2}=0\)có nghiệm là:
A.\(x=\pm\frac{\pi}{4}+k2\pi\)
B.\(x=\frac{\pi}{2}+k\pi\)
C.\(x=\frac{\pi}{4}+k\pi\)
D.\(x=\frac{\pi}{4}+k2\pi\)
Nghiệm của phương trình \(sin^4x+cos^4x+cos\left(x-\dfrac{\pi}{4}\right).sin\left(3x-\dfrac{\pi}{4}\right)-\dfrac{3}{2}=0\)
2. CM:
a1) \(\dfrac{\sin110}{\cos110}\)+ \(\dfrac{\cos20}{\sin20}\)=0
a2) sin2x + sin2(\(\dfrac{\pi}{3}\)-x) + sinx . sin(\(\dfrac{\pi}{3}\)-x)= \(\dfrac{3}{4}\)
a3) sin2x + cos(\(\dfrac{\pi}{3}\)-x).cos(\(\dfrac{\pi}{3}\)+x) = \(\dfrac{3}{4}\)
cos(x+pi/3)+sin(3x+pi/4)=0