Question

[Mai Thị Thanh Xuân]

Chứng minh rằng khi góc \(\alpha\) nhọn thì :

a) \(\sin2\alpha=2\sin\alpha\cos\alpha\)

b) \(\cos2\alpha=1-2\sin^2\alpha\)

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(\sin2a=\sin\left(a+a\right)\)

\(=\sin a\cdot\cos a+\cos a\cdot\sin a\)

\(=2\sin a\cdot\cos a\)

b: \(\cos2a=\cos^2a-\sin^2a\)

\(=1-\sin^2a-\sin^2a\)

\(=1-2\sin^2a\)