Các câu hỏi tương tự
CMR: \(\frac{\sin^4\alpha-\cos^2\alpha+2\cos^4\alpha-\cos^6\alpha}{\cos^4\alpha-\sin^2\alpha+2\sin^4\alpha-\sin^6\alpha}=\tan^6\alpha\)
Cho \(\tan\alpha=\dfrac{3}{5}\). Tính giá trị của các biểu thức sau:
M=\(\dfrac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)
N=\(\dfrac{\sin\alpha\times\cos\alpha}{\sin^2\alpha-\cos^2\alpha}\)
Chứng minh các hệ thức sau:
a) \(\frac{1-cos\alpha}{sin\alpha}=\frac{sin\alpha}{1+cos\alpha}\)
b) \(tan^2\alpha-sin^2\alpha=tan^2\alpha.sin^2\alpha\)
c) \(\frac{1-tan\alpha}{1+tan\alpha}=\frac{cos\alpha-sin\alpha}{cos\alpha+sin\alpha}\)
Cho tan \(\alpha\)=\(\frac{3}{5}\). Tính
A= \(\frac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)
B=\(\frac{\sin\alpha\cdot\cos\alpha}{\sin^2\alpha-\cos^2\alpha}\)
C=\(\frac{\sin^3\alpha\cdot\cos^3\alpha}{2\sin\alpha\cdot\cos^2\alpha+\cos\alpha\cdot\sin^2\alpha}\)
Giúp mình với . MÌnh cảm ơn
2) Rút gọna)1-sin^22b)left(1-cosalpharight)left(1+cosalpharight)c)1+sin^2alpha+cos^2alphad)sinalpha-sinalpha.cos^2alphae)sin^2alpha+cos^2alpha+2sin^2alpha.cos^2alphaf)tan^2alpha-sin^2alpha.tan^2alphag)cos^2alpha+tan^2alpha.cos^2alphah)tan^2alphaleft(2cos^2alpha+sin^2alpha-1right)
Đọc tiếp
2) Rút gọn
a)\(1-\sin^22\)
b)\(\left(1-\cos\alpha\right)\left(1+\cos\alpha\right)\)
c)\(1+\sin^2\alpha+\cos^2\alpha\)
d)\(\sin\alpha-\sin\alpha.\cos^2\alpha\)
e)\(\sin^2\alpha+\cos^2\alpha+2\sin^2\alpha.\cos^2\alpha\)
f)\(\tan^2\alpha-\sin^2\alpha.\tan^2\alpha\)
g)\(\cos^2\alpha+\tan^2\alpha.\cos^2\alpha\)
h)\(\tan^2\alpha\left(2\cos^2\alpha+\sin^2\alpha-1\right)\)
Chứng minh:
a) \(\tan^2\alpha-\sin^2\alpha=\tan^2\alpha.\sin^2\alpha\)
b) \(\frac{1-\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{17\cos\alpha}\)
1. Tìm x, biết: a. tan x+cot x2b. sin x.cos xfrac{sqrt{3}}{4}2. a. Biết tanalphafrac{1}{3}Tính Afrac{sinalpha-cosalpha}{sinalpha+cosalpha}b. Biết sinalphafrac{2}{3}Tính B3.sin^2alpha+4.cos^2alphac. Tính Csin^210^o+sin^220^o+sin^270^o+sin^280^od. Tính Dtan20^o.tan35^o.tan55^o.tan70^oe. Tính Esin^6alpha+cos^6alpha+3.sin^2alpha.cos^2alphaf. Tính F3.left(sin^3alpha+cos^3alpharight)-2.left(sin^6alpha+cos^6alpharight)g. Tính Gsqrt{sin^4alpha+4.cos^2alpha}+sqrt{cos^4alpha+4.sin^2alpha}Mọi người giúp mì...
Đọc tiếp
1. Tìm x, biết:
a. \(\tan x+\cot x=2\)
b. \(\sin x.\cos x=\frac{\sqrt{3}}{4}\)
2.
a. Biết \(\tan\alpha=\frac{1}{3}\)Tính A=\(\frac{\sin\alpha-\cos\alpha}{\sin\alpha+\cos\alpha}\)
b. Biết \(\sin\alpha=\frac{2}{3}\)Tính B=\(3.\sin^2\alpha+4.\cos^2\alpha\)
c. Tính C=\(\sin^210^o+\sin^220^o+\sin^270^o+\sin^280^o\)
d. Tính D=\(\tan20^o.\tan35^o.\tan55^o.\tan70^o\)
e. Tính E=\(\sin^6\alpha+\cos^6\alpha+3.\sin^2\alpha.\cos^2\alpha\)
f. Tính F=\(3.\left(\sin^3\alpha+\cos^3\alpha\right)-2.\left(\sin^6\alpha+\cos^6\alpha\right)\)
g. Tính G=\(\sqrt{\sin^4\alpha+4.\cos^2\alpha}+\sqrt{\cos^4\alpha+4.\sin^2\alpha}\)
Mọi người giúp mình với. Mình cảm ơn ạ!
CMR: \(\frac{\sin^2\alpha}{\cos\alpha\left(1+\tan\alpha\right)}-\frac{\cos^2\alpha}{\sin\alpha\left(1+\cot\alpha\right)}=\sin\alpha-\cos\alpha\)
\(cos^225-\sin23+\cos67-\frac{3\tan54}{\cot36}+\cos^265\)\(\sin^4\alpha+\cos^4\alpha+2\sin\alpha.\cos\alpha\)\(tan^2\alpha\left(2cos^2\alpha+sin^2\alpha-1\right)\)\(\left(\tan\alpha+\cot\alpha\right)^2-\left(\tan\alpha-\cot\alpha\right)^2\)
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