证明 sin^2(a)-cos^2(a)=1-2cos^2(a)

解答

证明

sin^{2} (a) - cos^{2} (a) = 1 - 2 cos^{2} (a)

真

求解步骤

sin^{2} (a) - cos^{2} (a) = 1 - 2 cos^{2} (a)

调整左侧

sin^{2} (a) - cos^{2} (a)

使用三角恒等式改写

sin^{2} (a) - cos^{2} (a)

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= 1 - cos^{2} (a) - cos^{2} (a)

p ro v e tan (2 A) - 2 tan (2 A) sin^{2} (A) = sin (2 A)

p ro v e sin^{2} (x) = \frac{1}{csc ^{2} ( x )}

p ro v e \frac{cot ( 4 u ) - 1}{cot ( 4 u ) + 1} = \frac{1 - tan ( 4 u )}{1 + tan ( 4 u )}

p ro v e sin (- x) = sin (x - π)

p ro v e sin (4 a) = 4 sin (a) cos (a) cos (2 a)