\(=\dfrac{1}{\sin a}+\dfrac{\sin a}{1+\cos a}\)
\(=\dfrac{1+\cos a+\sin^2a}{\sin a\left(1+\cos a\right)}\)
\(=\dfrac{1+\cos a+1-\cos^2a}{\sin a\left(1+\cos a\right)}\)
\(=\dfrac{-\cos^2a+\cos a+2}{\sin a\left(1+\cos a\right)}\)
\(=\dfrac{-\left(\cos^2a-\cos a-2\right)}{\sin a\left(\cos a+1\right)}\)
\(=\dfrac{-\left(\cos a-2\right)}{\sin a}\)
a) Biết Sin α.cos α=\(\dfrac{12}{25}\). Tính tỉ số lượng giác của góc α
b) Biết Sin α=\(\dfrac{3}{5}\). Tính A=5.Sin2α + 6cos2α
c) Biết cot α=\(\dfrac{4}{3}\). Tính D=\(\dfrac{Sin\alpha+cos\alpha}{Sin\alpha-cos\alpha}\)
Chứng minh:
a)\(cot^2\alpha-cos^2\alpha\cdot cot^2\alpha=cos^2\alpha\)
b)\(tan^2\alpha-sin^2\alpha\cdot tan^2\alpha=sin^2\alpha\)
c) \(\dfrac{1-cos^2}{sin\alpha}\) = \(\dfrac{sin\alpha}{1+cos\alpha}\)
d)\(tan^2\alpha-sin^2\alpha=tan^2\cdot sin^2\alpha\)
e) \(\sin^6\alpha+cos^6\alpha+3sin^2\cdot cos^2\alpha=1\)
Cho \(\cot\alpha=\dfrac{1}{3}\). Tính giá trị biểu thức \(Q=\dfrac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha}\)
a) Biết \(\sin\alpha=\dfrac{9}{15}\). Tính \(\cos\alpha,\tan\alpha,\cot\alpha\)
b) Biết \(\cos\alpha=\dfrac{3}{5}\). Tính\(\sin\alpha,\tan\alpha,\cot\alpha\)
CMR:
\(a.tan^2\alpha+1=\dfrac{1}{cos^2\alpha}\)
b)\(cot^2\alpha+1=\dfrac{1}{sin^2\alpha}\)
c)\(cos^4\alpha-sin^4\alpha=2cos^2\alpha-1\)
CM các hệ thức sau:
a) \(1+\tan^2\alpha=\frac{1}{\cos^2\alpha}\)
b) \(1+\cot^2\alpha=\frac{1}{\sin^2\alpha}\)
c) \(\cot^2\alpha-\cos^2\alpha=\cot^2\alpha.\cos^2\alpha\)
d) \(\frac{1+\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\)
CMR
a)\(\frac{1+\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\)
b)\(\frac{\tan\alpha+1}{\tan\alpha-1}=\frac{1+\cot\alpha}{1-\cot\alpha}\)
c) \(\tan^2\alpha-\sin^2\alpha=\tan^2\alpha.\sin^2\alpha\)
d)\(\frac{1-4\sin^2\alpha.\cos^2\alpha}{\left(\sin\alpha-\cos\alpha\right)^2}=\left(\sin\alpha+\cos\alpha\right)^2\)
1)
a) cot2 α+ 1 = \(\dfrac{1}{sin^2a}\)
b)1 + tan2 α = \(\dfrac{1}{cos^2a}\)
c) sin4 α+ cos2α = 2.sin2α . cos2 α
d) \(\dfrac{1-4.sin^2a.cos^2a}{\left(sina+cosa\right)^2}=1-2.sina.cosa\)
e) \(\dfrac{2.sina.cosa-1}{cos^2a-sin^2a}=\dfrac{tana-1}{tana+1}\)
Cho Tan α =\(\dfrac{3}{4}\).Tìm sin α ,cos α ,cot α
