Chứng minh rằng:
----- Nội dung dịch tự động từ ảnh -----
Bài 12 Chứng minh rằng
a) \(\frac{\sin^3 \alpha + \cos^3 \alpha}{\sin \alpha + \cos \alpha} = 1 - \sin \alpha \cdot \cos \alpha\)
b) \(\frac{\sin^2 \alpha - \cos^2 \alpha}{1 + 2 \sin \alpha \cdot \cos \alpha} = \tan \alpha - 1\)
c) \(\sin^4 \alpha + \cos^4 \alpha - \sin^6 \alpha - \cos^6 \alpha = \sin^2 \alpha \cdot \cos^2 \alpha\)
d) \(3(\cos^4 \alpha + \sin^4 \alpha) - 2(\cos^6 \alpha + \sin^6 \alpha) = 1\)
e) \(\frac{\sin a}{1 + \cos a} + \frac{1 + \cos a}{\sin a} = \frac{2}{\sin a}\)
Bài 12 Chứng minh rằng
a) \(\frac{\sin^3 \alpha + \cos^3 \alpha}{\sin \alpha + \cos \alpha} = 1 - \sin \alpha \cdot \cos \alpha\)
b) \(\frac{\sin^2 \alpha - \cos^2 \alpha}{1 + 2 \sin \alpha \cdot \cos \alpha} = \tan \alpha - 1\)
c) \(\sin^4 \alpha + \cos^4 \alpha - \sin^6 \alpha - \cos^6 \alpha = \sin^2 \alpha \cdot \cos^2 \alpha\)
d) \(3(\cos^4 \alpha + \sin^4 \alpha) - 2(\cos^6 \alpha + \sin^6 \alpha) = 1\)
e) \(\frac{\sin a}{1 + \cos a} + \frac{1 + \cos a}{\sin a} = \frac{2}{\sin a}\)