8 tháng 4 2022 lúc 9:43
§3. Công thức lượng giác
Các câu hỏi tương tự
Rút gọn cac biểu thức sau:Asinleft(dfrac{5pi}{2}-alpharight)+cosleft(13pi+alpharight)-3sinleft(alpha-5piright)Bsinleft(x+dfrac{85pi}{2}right)+cosleft(2017pi+xright)+sin^2left(33pi+xright)+sin^2left(x-dfrac{5pi}{2}right)+cosleft(x+dfrac{3pi}{2}right)Csinleft(x+dfrac{2017pi}{2}right)+2sin^2left(x-piright)+cosleft(x+2019piright)+cos2x+sinleft(x+dfrac{9pi}{2}right)
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Rút gọn cac biểu thức sau:
\(A=sin\left(\dfrac{5\pi}{2}-\alpha\right)+cos\left(13\pi+\alpha\right)-3sin\left(\alpha-5\pi\right)\)
\(B=sin\left(x+\dfrac{85\pi}{2}\right)+cos\left(2017\pi+x\right)+sin^2\left(33\pi+x\right)+sin^2\left(x-\dfrac{5\pi}{2}\right)+cos\left(x+\dfrac{3\pi}{2}\right)\)\(C=sin\left(x+\dfrac{2017\pi}{2}\right)+2sin^2\left(x-\pi\right)+cos\left(x+2019\pi\right)+cos2x+sin\left(x+\dfrac{9\pi}{2}\right)\)
Chứng minh đẳng thức:1 ,tanleft(dfrac{pi}{4}+dfrac{x}{2}right)+cotleft(dfrac{pi}{4}+dfrac{x}{2}right)dfrac{2}{cosx}2 ,sin^8x-cos^8x-left(dfrac{7}{8}cos2x+dfrac{1}{8}cos6xright)3 ,3-4cos2x+cos4x8sin^4x4 ,sinleft(2x+dfrac{pi}{3}right).cosleft(x-dfrac{pi}{6}right)-cosleft(2x+dfrac{pi}{3}right).cosleft(dfrac{2pi}{3}-xright)cosx5 ,sqrt{3}cos2x+sin2x+sinleft(4x-dfrac{pi}{3}right)4cosleft(2x-dfrac{pi}{6}right).sin^2left(x+dfrac{pi}{6}right)
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Chứng minh đẳng thức:
1 ,\(tan\left(\dfrac{\pi}{4}+\dfrac{x}{2}\right)+cot\left(\dfrac{\pi}{4}+\dfrac{x}{2}\right)=\dfrac{2}{cosx}\)
2 ,\(sin^8x-cos^8x=-\left(\dfrac{7}{8}cos2x+\dfrac{1}{8}cos6x\right)\)
3 ,\(3-4cos2x+cos4x=8sin^4x\)
4 ,\(sin\left(2x+\dfrac{\pi}{3}\right).cos\left(x-\dfrac{\pi}{6}\right)-cos\left(2x+\dfrac{\pi}{3}\right).cos\left(\dfrac{2\pi}{3}-x\right)=cosx\)
5 ,\(\sqrt{3}cos2x+sin2x+sin\left(4x-\dfrac{\pi}{3}\right)=4cos\left(2x-\dfrac{\pi}{6}\right).sin^2\left(x+\dfrac{\pi}{6}\right)\)
Cho x+2y=\(\dfrac{\Pi}{2}\). Rút gọn biểu thức:
\(A=\dfrac{Cos\left(x+y\right)-Cosy}{Cos\left(x+y\right)+Cosy}\)
Chứng minh các biểu thức sau không phụ thuộc vào x:1, A3left(sin^4x+cos^4xright)-2left(sin^6x+cos^6xright)2, Bcos^6x+2sin^4x.cos^2x+3sin^2x.cos^4x+sin^4x3, Ccosleft(x-dfrac{pi}{3}right).cosleft(x+dfrac{pi}{4}right)+cosleft(x+dfrac{pi}{6}right).cosleft(x+dfrac{3pi}{4}right)4, Dcos^2x+cos^2left(x+dfrac{2pi}{3}right)+cos^2left(dfrac{2pi}{3}-xright)5, E2left(sin^4x+cos^4x+sin^2x.cos^2xright)-left(sin^8x+cos^8xright)6, Fcosleft(pi-xright)+sinleft(dfrac{-3pi}{2}+xright)-tanleft(dfrac{pi}{2}+xright).c...
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Chứng minh các biểu thức sau không phụ thuộc vào x:
1, \(A=3\left(sin^4x+cos^4x\right)-2\left(sin^6x+cos^6x\right)\)
2, \(B=cos^6x+2sin^4x.cos^2x+3sin^2x.cos^4x+sin^4x\)
3, \(C=cos\left(x-\dfrac{\pi}{3}\right).cos\left(x+\dfrac{\pi}{4}\right)+cos\left(x+\dfrac{\pi}{6}\right).cos\left(x+\dfrac{3\pi}{4}\right)\)
4, \(D=cos^2x+cos^2\left(x+\dfrac{2\pi}{3}\right)+cos^2\left(\dfrac{2\pi}{3}-x\right)\)
5, \(E=2\left(sin^4x+cos^4x+sin^2x.cos^2x\right)-\left(sin^8x+cos^8x\right)\)
6, \(F=cos\left(\pi-x\right)+sin\left(\dfrac{-3\pi}{2}+x\right)-tan\left(\dfrac{\pi}{2}+x\right).cot\left(\dfrac{3\pi}{2}-x\right)\)
Rút gọn các biểu thức :
a) \(\sin\left(a+b\right)+\sin\left(\dfrac{\pi}{2}-a\right)\sin\left(-b\right)\)
b) \(\cos\left(\dfrac{\pi}{4}+a\right)\cos\left(\dfrac{\pi}{4}-a\right)+\dfrac{1}{2}\sin^2a\)
c) \(\cos\left(\dfrac{\pi}{2}-a\right)\sin\left(\dfrac{\pi}{2}-b\right)-\sin\left(a-b\right)\)
Rút gọn biểu thức S=sin\(\left(x+\dfrac{2017\pi}{2}\right)\)+2sin2(x-\(\pi\)) +cos(x+2019π)+cos2x
1. Cho 2cosleft(alpha+betaright)cosalphacosleft(pi+betaright)Tính Adfrac{1}{2sin^2alpha+3cos^2alpha}+dfrac{1}{2sin^2beta+3cos^2beta}2. Rút gọn: a) A4cosdfrac{2x}{3}cosdfrac{pi+2x}{3}cosdfrac{pi-2x}{3}b) Bdfrac{sinleft(a-bright).sinleft(a+bright)}{cos^2a.sin^2b}-tan^2a.cot^2b3. Chứng minh rằng: Nếu 2tan atanleft(a+bright) thì:a) sin bsin a.cosleft(a+bright)b) 3sin bsinleft(2a+bright)
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1. Cho \(2\cos\left(\alpha+\beta\right)=\cos\alpha\cos\left(\pi+\beta\right)\)
Tính \(A=\dfrac{1}{2\sin^2\alpha+3\cos^2\alpha}+\dfrac{1}{2\sin^2\beta+3\cos^2\beta}\)
2. Rút gọn: a) \(A=4\cos\dfrac{2x}{3}\cos\dfrac{\pi+2x}{3}\cos\dfrac{\pi-2x}{3}\)
b) \(B=\dfrac{\sin\left(a-b\right).\sin\left(a+b\right)}{\cos^2a.\sin^2b}-\tan^2a.\cot^2b\)
3. Chứng minh rằng: Nếu \(2\tan a=\tan\left(a+b\right)\) thì:
a) \(\sin b=\sin a.\cos\left(a+b\right)\)
b) \(3\sin b=\sin\left(2a+b\right)\)
Chứng minh đẳng thức :
a) \(\dfrac{\cos\left(a-b\right)}{\cos\left(a+b\right)}=\dfrac{\cot a.\cot b+1}{\cot a.\cot b-1}\)
b) \(\sin\left(a+b\right)\sin\left(a-b\right)=\sin^2a-\sin^2b=\cos^2b-\cos^2a\)
c) \(\cos\left(a+b\right)\cos\left(a-b\right)=\cos^2a-\sin^2b=\cos^2b-\sin^2a\)
cho \(\sin x+\cos x=\dfrac{1}{5}\), \(x\in\left(\dfrac{\pi}{2};\pi\right)\) . Tính B = sin^5 (x) + cos^3 (x)