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=\(\dfrac{\sin\alpha\times\cos\alpha}{\sin^2\alpha-\cos^2\alpha}\)
Cho góc nhọn \(\alpha\). Tính giá trị biểu thức:
a) \(A=\left(\sin\alpha+\cos\alpha\right)^2+\left(\sin\alpha-\cos\alpha\right)^2\)
b) \(B=\sin^4\alpha\left(1+2\cos^2\alpha\right)+\cos^4\alpha\left(1+2\sin^2\alpha\right)\)
c) \(C=\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha.\cos^2\alpha\)
d)\( D=\left(3\sin\alpha+4\cos\alpha\right)^2+\left(4\sin\alpha-3\cos\alpha\right)^2\)
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
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!
Cho \(\tan\alpha=\frac{3}{5}\)
Tính: \(\frac{\sin^3\alpha+\cos^3\alpha}{2\sin\alpha.\cos^2\alpha+\cos\alpha.\sin^2\alpha}\)
Cho góc nhọn \(\alpha\)thỏa mãn \(\tan\alpha=\frac{2}{\sqrt{3}}\). Tính: \(B=\frac{\cos^4\alpha+\sin^2\alpha\left(\cos^2\alpha+1\right)}{2\cos^4\alpha+2\sin^2\cos^2-\frac{3}{5}\sin^2\alpha}\)
tính :
\(E=\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha\cdot\cos^2\alpha\)
\(F=3\sin^3\alpha+\cos^3\alpha-2\sin^6\alpha+\cos^6\alpha\)
\(G=\sqrt{\sin^4\alpha+4\cos^2\alpha}+\sqrt{\cos^4\alpha+4\sin^2\alpha}\)
tính
a) \(\tan^2\alpha-\sin^2\alpha-\tan^2\alpha\times\sin^2\alpha\)
b)\(\frac{sin^4\alpha-cos^4\alpha}{sin\alpha+cos\alpha}-sin\alpha+cos\alpha\)
\(\tan\alpha=2\). Hãy tính GTBT:
a/ \(\frac{\sin\alpha+5\cos\alpha}{2\sin\alpha-3\cos\alpha}\)
b/\(\sin^2\alpha+2\sin\alpha.\cos\alpha-5\cos^2\alpha\)
