Đặt \(\frac{\pi}{24}=x\)
\(B=cos^23x+sin5x.sinx=cos^23x-\frac{1}{2}\left(cos6x-cos4x\right)\)
\(=\frac{1}{2}+\frac{1}{2}cos6x-\frac{1}{2}cos6x+\frac{1}{2}cos4x\)
\(=\frac{1}{2}+\frac{1}{2}cos4x\)
\(=\frac{1}{2}+\frac{1}{2}cos\left(\frac{4\pi}{24}\right)=\frac{1}{2}+\frac{1}{2}cos\frac{\pi}{6}\)
\(=\frac{1}{2}+\frac{\sqrt{3}}{4}\)
Chứng minh (giúp mình với)
\(cos\frac{33\pi}{16}.sin\frac{5\pi}{16}.cos\frac{5\pi}{16}.cos\frac{7\pi}{16}=\frac{\sqrt{2}}{6}\)
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) \(B=2sin\left(\frac{\pi}{2}+x\right)+sin\left(5\pi-x\right)+sin\left(\frac{3\pi}{2}+x\right)+cos\left(\frac{\pi}{2}+x\right)\)
sin\(\left(x+\frac{85\Pi}{2}\right)+cos\left(207\Pi+x\right)+sin^2\left(33\Pi+x\right)+sin^2\left(x-\frac{3\Pi}{2}\right)\)
chứng minh rằng
a) \(cos^4a+sin^4a-6sin^2a.cos^2a=cos4a\)
b) \(tan\frac{3\pi}{5}-tan\frac{2\pi}{5}-tan\frac{\pi}{5}=tan\frac{\pi}{5}.tan\frac{2\pi}{5}.tan\frac{3\pi}{5}\)
\(\cos\left(5\Pi+x\right)+\sin\left(\frac{9\Pi}{2}-x\right)-\tan\left(\frac{3\Pi}{2}+x\right)\cot\left(\frac{3\Pi}{2}-x\right)\)
Rút gọn: A=cos(\(\frac{3\pi}{2}-a\)) - sin(\(\frac{3\pi}{2}-a\)) + cos(\(a-\frac{7\pi}{2}\)) - sin(a-\(\frac{7\pi}{2}\))
giải chi tiết giúp mình với :)
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,\(\cos x-\sin x=\sqrt{2}\cos\left(x+\frac{\pi}{4}\right)\)
Rút gọn
a)cos (\(\frac{\pi}{2}\)+\(\alpha\))
b) sin(\(\alpha\)+5\(\pi\))
c)sin(\(\frac{3\pi}{2}\)-\(\alpha\))
d)sin(\(\frac{3\pi}{2}\)+\(\alpha\))
Biết \(sin\alpha=\frac{3}{5}\) và \(\frac{\pi}{2}< \alpha< \pi\). Tính \(P=1-2sin^2\left(\frac{\pi}{4}-\alpha\right)+sin2\alpha+cos\left(\pi-2\alpha\right)-6tan\left(\frac{\pi}{2}-\alpha\right)\)
