\(tana=\frac{1}{2}\)
\(\Rightarrow\frac{sina}{cosa}=\frac{1}{2}\)
\(2sina=cosa\)
\(A=\frac{sina+cosa}{cosa-sina}\)
\(=\frac{sina+2sina}{2sina-sina}\)
\(=\frac{3sina}{sina}=3\)
\(tana=\frac{1}{2}\)
\(\Rightarrow\frac{sina}{cosa}=\frac{1}{2}\)
\(2sina=cosa\)
\(A=\frac{sina+cosa}{cosa-sina}\)
\(=\frac{sina+2sina}{2sina-sina}\)
\(=\frac{3sina}{sina}=3\)
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 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 \(\tan\alpha=3\). Tính
a) \(\dfrac{2\sin\alpha+3\cos\alpha}{3\sin\alpha-4\cos\alpha}.\)
b) \(\dfrac{\sin\alpha\cos\alpha}{\sin^2\alpha-\sin\alpha\cos\alpha+\cos^2\alpha}.\)
f) Cho α, Blà hai góc nhọn. Chứng minh rằng:
\(\cos^2\alpha-\cos^2\beta=\sin^2\alpha-\sin^2\beta=\dfrac{1}{1+\tan^2\alpha}-\dfrac{1}{1+tan^2\beta}\)
Câu 50**: Cho góc nhọn tuỳ ý giá trị biểu thức \(\dfrac{tan\alpha}{cot\alpha}+\dfrac{cot\alpha}{tan\alpha}-\dfrac{sin^2\alpha}{cos^2\alpha}\) bằng
A. \(tan^2\alpha\) ; B . \(cot^2\alpha\) ; C . 0 ; D. 1 .
Câu 50**: Cho góc nhọn α tuỳ ý giá trị biểu thức \(\dfrac{tan\alpha}{cot\alpha}+\dfrac{cot\alpha}{tan\alpha}-\dfrac{sin^2\alpha}{cos^2\alpha}\)bằng
A. \(tan^2\alpha\) ; B . \(cot^2\) α ; C . 0 ; D. 1 .
giải hộ mik vs
tính
a) \(\tan^2\alpha-\sin^2\alpha-\tan^2\alpha\times\sin^2\alpha\)
b)\(\frac{sin^4\alpha-cos^4\alpha}{sin\alpha+cos\alpha}-sin\alpha+cos\alpha\)
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) \(\frac{1-tan\alpha}{1+tan\alpha}=\frac{cos\alpha-sin\alpha}{cos\alpha+sin\alpha}\)
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)\(\tan^2\alpha\left(2\cos^2\alpha+\sin^2\alpha-1\right)\)