证明 sin(2a)=2cos(a)sin(a)

解答

证明

sin (2 a) = 2 cos (a) sin (a)

真

求解步骤

sin (2 a) = 2 cos (a) sin (a)

调整左侧

sin (2 a)

使用三角恒等式改写

sin (2 a)

改写为

= sin (a + a)

使用角和恒等式:

sin (s + s) = sin (s) cos (s) + cos (s) sin (s)

= sin (a) cos (a) + cos (a) sin (a)

= sin (a) cos (a) + cos (a) sin (a)

化简

sin (a) cos (a) + cos (a) sin (a) : 2 sin (a) cos (a)

sin (a) cos (a) + cos (a) sin (a)

p ro v e sin (2 α) = \frac{2 tan ( α )}{1 + tan ^{2} ( α )}

p ro v e cot (x) sec (x) csc^{2} (x) - cot^{3} (x) sec (x) = csc (x)

p ro v e csc (t) - sin (t) = cot (t) cos (t)

p ro v e cos (6 0^{\circ}) = 2 cos^{2} (3 0^{\circ}) - 1

p ro v e (sin (t) + cos (t))^{2} = 1 + sin (2 t)