chứng minh các đẳng thức sau
a) \(\dfrac{1-cos\alpha}{sin\alpha}=\dfrac{sin\alpha}{1+cos\alpha}\)
b)\(\dfrac{cos\alpha}{1+sin\alpha}+tg\alpha=\dfrac{1}{cos\alpha}\)
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=\(\dfrac{\sin\alpha\times\cos\alpha}{\sin^2\alpha-\cos^2\alpha}\)
f) Cho α, Blà hai góc nhọn. Chứng minh rằng:
\(\cos^2\alpha-\cos^2\beta=\sin^2\alpha-\sin^2\beta=\dfrac{1}{1+\tan^2\alpha}-\dfrac{1}{1+tan^2\beta}\)
1. Chứng minh rằng: \(\frac{1-2\sin.\cos\alpha}{sin^2\alpha-\cos^2\alpha}=\frac{sin\alpha-\cos\alpha}{sin\alpha+\cos\alpha}\) (\(\alpha\ne45^o\))
2. Chứng minh: \(\cos^4\alpha+\sin^2\alpha.\cos^2\alpha+\sin^2\alpha\) không phụ thuộc vào x
Cho tan \(\alpha\) = \(\dfrac{1}{2}\) . Tính A= \(\dfrac{sin\alpha+cos\alpha}{cos\alpha - sin\alpha}\)
Cho \(\tan\alpha=3\). Tính
a) \(\dfrac{2\sin\alpha+3\cos\alpha}{3\sin\alpha-4\cos\alpha}.\)
b) \(\dfrac{\sin\alpha\cos\alpha}{\sin^2\alpha-\sin\alpha\cos\alpha+\cos^2\alpha}.\)
Chứng minh:
a)\(\cos^4\alpha-sin^4\alpha=2cos^2\alpha-1\)
b)\(\frac{cos\alpha}{1-sin\alpha}=\frac{1+sin\alpha}{cos\alpha}\)
c)\(\frac{\left(sin\alpha+cos\alpha\right)^2-\left(sin\alpha-cos\alpha\right)^2}{sin\alpha.cos\alpha}=4\)
Mình cần gấp!!!
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) \(\frac{1-tan\alpha}{1+tan\alpha}=\frac{cos\alpha-sin\alpha}{cos\alpha+sin\alpha}\)
Rút gọn:
A= \(\sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)
B= \(\left(cos\alpha-sin\alpha\right)^2+\left(cos\alpha+sin\alpha\right)^2\)
C= \(\dfrac{\left(cos\alpha-sin\alpha\right)^2-\left(cos\alpha+sin\alpha\right)^2}{sin\alpha.cos\alpha}\)