Cho \(m\sin\left(a+b\right)=\cos\left(a-b\right),\left|m\right|\ne1,\sin\left(a-b\right)\ne0.\)Chứng minh rằng: \(\frac{1}{1-m\sin2a}+\frac{1}{1-m\sin2b}=\frac{2}{1-m}\)
Chứng minh đẳng thức
\(2sin\left(\frac{\pi}{2}+x\right)+sin\left(3\pi-x\right)+sin\left(\frac{3\pi}{2}+x\right)+cos\left(\frac{\pi}{2}+x\right)=cosx\)
Cho: cosa, cosb ≠ 0, chứng minh đẳng thức: \(\frac{\sin\left(a+b\right).\sin\left(a-b\right)}{\cos^2a.\cos^2b}=\tan^2a-\tan^2b\)
Cho \(sin\left(x-y\right)=\frac{1}{2}\). Chứng minh: \(1-\sin^2x-\sin^2y+2\sin x.\sin y.\cos\left(x-y\right)=\frac{3}{4}\)
Chứng minh|
a) \(\frac{1+sin2x}{sinx+cosx}-\frac{1-tan^2\frac{x}{2}}{1+tan^2\frac{x}{2}}=sinx\)
b) \(sin^4x+cos^4\left(x+\frac{\pi}{4}\right)=\frac{3}{4}-\frac{\sqrt{2}}{2}sin\left(2x+\frac{\pi}{4}\right)\)
Chứng minh
a) \(2sin\left(\frac{\pi}{4}+a\right)sin\left(\frac{\pi}{4}-a\right)=cos2a\)
b) \(tanx-\frac{1}{tanx}=-\frac{2}{tan2x}\)
Câu 1: Chứng minh
\(\cos5x.\cos3x+\sin7x.\sin x=\cos2x.\cos4x\)
\(\frac{1-2\sin^22x}{1-\sin4x}=\frac{1+\tan2x}{1-\tan2x}\)
Câu 2:Rút gọn biểu thức
\(2\cos x-3\cos\left(\pi-x\right)+5\sin\left(\frac{7\pi}{x}-x\right)+cot\left(\frac{3\pi}{2}-x\right)\)
Chứng minh
a) \(sin^4x=\frac{3}{8}-\frac{1}{2}cos2x+\frac{1}{8}cos4x\)
b) \(\frac{cos\left(a+b\right)cos\left(a-b\right)}{cos^2a.cos^2b}=1-tan^2a.tan^2b\)
Câu 1 : chứng minh rằng : \(\frac{sina+sin2a+sin3a}{cosa+cos2a+cos3a}=tan2a\)
Câu 2 : chứng minh : \(cos^2\left(\alpha-\frac{\pi}{4}\right)-sin^2\left(\alpha-\frac{\pi}{4}\right)=sin2\alpha\)
