1.cho sin \(\alpha\)= \(\frac{1}{2}\) tính P = \(\sqrt{2}\) (1+cot \(\alpha\))cos(\(\frac{\pi}{4}\)+2)
1. Cho α + β + f = π . CM:
a1) sinα + sinβ +sinf = 4.cos\(\dfrac{\alpha}{2}\) .cos\(\dfrac{\beta}{2}\). cos\(\dfrac{f}{2}\)
a2) cosα + cosβ +cosf = 1+ 4sin\(\dfrac{\alpha}{2}\).sin\(\dfrac{\beta}{2}\).sin\(\dfrac{f}{2}\)
Các bạn giúp mình với ạ
Cho cotα=2. Giá trị của biểu thức P=\(\frac{sin\alpha+cos\alpha}{sin\alpha—cos\alpha}\)
phương trình \(\frac{\left(1+\sin x+\cos2x\right)\sin\left(x+\frac{\pi}{4}\right)}{1+\tan x}=\frac{1}{\sqrt{2}}\cos\) có các nghiệm dạng x=\(\alpha+k2;\beta+k2\pi;\alpha\ne\beta;k\in Z;-\pi\le\alpha;\beta\le\pi\) tính \(\alpha^2+\beta^2\)
Cho \(5\sin2\alpha-6\cos\alpha=0\) và \(0< \alpha< \dfrac{\pi}{2}\)
Tính A = \(\cos(\dfrac{\pi}{2}-\alpha)+\sin\left(2017\pi-\alpha\right)-\cot(2018\pi+\alpha)\)
Cho góc \(\alpha\) thỏa mãn : \(\frac{\pi}{2}
giải các pt
a) \(sin\left(\frac{3\pi}{10}-\frac{x}{2}\right)=\frac{1}{2}sin\left(\frac{\pi}{10}+\frac{3x}{2}\right)\)
b) \(4\left(sin^2x+\frac{1}{sin^2x}\right)+4\left(sinx+\frac{1}{sinx}\right)=7\)
c) \(9\left(\frac{2}{cosx}+cosx\right)+2\left(cos^2x+\frac{4}{cos^2x}\right)=1\)
d) \(2\left(cos^2x+\frac{4}{cos^2x}\right)+9\left(\frac{2}{cosx}-cosx\right)=1\)
giải phương trình
\(\sin x\sqrt{1+2\sin x}=\cos2x\)
\(\sin\left(\frac{5x}{2}-\frac{\pi}{4}\right)-\cos\left(\frac{x}{2}-\frac{\pi}{4}\right)=\sqrt{2}\cos\frac{3x}{2}\)
\(3\sqrt{\tan x+1}\left(\sin x+2\cos x\right)=5\left(\sin x+3\cos x\right)\)
\(\sqrt{2}\left(\sin x+\sqrt{3}\cos x\right)=\sqrt{3}\cos2x-\sin2x\)
\(\sin2x\sin4x+2\left(3\sin x-4\sin^2x+1\right)=0\)
a. \(\cos^2\alpha+\cos^2\left(\alpha-\frac{\pi}{3}\right)+^{ }\cos^2\left(\frac{2\pi}{3}-\alpha\right)=\frac{3}{2}\)