\(sinx.sin\left(\frac{\pi}{3}-x\right)sin\left(\frac{\pi}{3}+x\right)=\frac{1}{2}sinx.\left[cos2x-cos\frac{2\pi}{3}\right]=\frac{1}{2}sinx\left(cos2x+\frac{1}{2}\right)\)
\(=\frac{1}{2}sinx.cos2x+\frac{1}{4}sinx=\frac{1}{4}\left(sin3x+sin\left(-x\right)\right)+\frac{1}{4}sinx\)
\(=\frac{1}{4}sin3x-\frac{1}{4}sinx+\frac{1}{4}sinx=\frac{1}{4}sin3x\)
sin\(\left(x+\frac{85\Pi}{2}\right)+cos\left(207\Pi+x\right)+sin^2\left(33\Pi+x\right)+sin^2\left(x-\frac{3\Pi}{2}\right)\)
Rút gọn các biểu thức sau:
1) \(A=2cosx+3cosx\left(\pi-x\right)-sin\left(\frac{7\pi}{2}-x\right)+tan\left(\frac{3\pi}{2}-x\right)\)
2) \(B=2sin\left(\frac{\pi}{2}+x\right)+sin\left(5\pi-x\right)+sin\left(\frac{3\pi}{2}+x\right)+cos\left(\frac{\pi}{2}+x\right)\)
Chứng minh rằng: (Pls help me)
a, \(\frac{1}{\sin x}+\cot x=\cot\frac{x}{2}\)
b, \(\frac{1-\cos x}{\sin x}=\tan\frac{x}{2}\)
c,\(\tan\frac{x}{2}\left(\frac{1}{\cos x}+1\right)=\tan x\)
d,\(\frac{\sin2a}{2\cos a\left(1+\cos a\right)}=\tan\frac{a}{2}\)
e,\(\cot x+\tan\frac{x}{2}=\frac{1}{\sin x}\)
f,\(3-4\cos2x+\cos4x=8\sin^4x\)
g,\(\frac{1-\cos x}{\sin x}=\frac{\sin x}{1+\cos x}\)
h,\(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\)
i,\(\sin x-\cos x=\sqrt{2}\sin\left(x-\frac{\pi}{4}\right)\)
l,\(\cos x-\sin x=\sqrt{2}\cos\left(x+\frac{\pi}{4}\right)\)
Tính giá trị biểu thức:
\(A=sin^2\frac{\pi}{3}+sin^2\frac{\pi}{9}+sin^2\frac{7\pi}{18}sin^2\frac{\pi}{6}\)
chứng minh các đẳng thức sau
a) \(\cos x\cos\left(\frac{\pi}{3}-x\right)\cos\left(\frac{\pi}{3}+x\right)=\frac{1}{4}\cos3x\)
b) \(\sin5x-2\sin x\left(\cos4x+\cos2x\right)=\sin x\)
chứng minh Q ko phụ thuộc vào x
P= sin2x + sin2\(\left(\frac{2\pi}{3}+x\right)\) + sin2 \(\left(\frac{2\pi}{3}-x\right)\)
help me
Chứng minh rằng:
a) \(sin\left(a+b\right).sin\left(a-b\right)=sin^2a-sin^2b=cos^2b-cos^2a\)
b) \(4sin\left(x+\dfrac{\Pi}{3}\right).sin\left(x-\dfrac{\Pi}{3}\right)=4sin^2x-3\)
c) \(sin\left(x+\dfrac{\Pi}{4}\right)-sin\left(x-\dfrac{\Pi}{4}\right)=\sqrt{2}cosx\)
d) \(\dfrac{1}{sin10^0}-\dfrac{\sqrt{3}}{cos10^0}=4\)
\(\cos\left(5\Pi+x\right)+\sin\left(\frac{9\Pi}{2}-x\right)-\tan\left(\frac{3\Pi}{2}+x\right)\cot\left(\frac{3\Pi}{2}-x\right)\)
chứng minh rằng
2) \(sin^2x+sin^2\left(\frac{\pi}{2}-x\right)-tan\left(\frac{\pi}{2}+x\right)tanx=2\)
Rút gọn: \(C=sin^2x+sin^2\left(\frac{\Pi}{3}-x\right)+sinx.sin\left(\frac{\Pi}{3}-x\right)\)
a/c giúp e vs ạ. e đang cần gấp ạ.
