证明 cot^2(x)+csc^2(x)=1+2cot^2(x)

解答

证明

cot^{2} (x) + csc^{2} (x) = 1 + 2 cot^{2} (x)

真

求解步骤

cot^{2} (x) + csc^{2} (x) = 1 + 2 cot^{2} (x)

调整左侧

cot^{2} (x) + csc^{2} (x)

使用三角恒等式改写

cot^{2} (x) + csc^{2} (x)

使用毕达哥拉斯恒等式:

csc^{2} (x) = 1 + cot^{2} (x)

= cot^{2} (x) + 1 + cot^{2} (x)

化简

cot^{2} (x) + 1 + cot^{2} (x) : 2 cot^{2} (x) + 1

cot^{2} (x) + 1 + cot^{2} (x)

对同类项分组

= cot^{2} (x) + cot^{2} (x) + 1

p ro v e \frac{tan ( y ) + cot ( y )}{csc ( y )} = sec (y)

p ro v e cos (3 B) = cos (B) (cos^{2} (B) - 3 sin^{2} (B))

p ro v e tan (2 x) = \frac{1}{1 - tan ( x )} - \frac{1}{1 + tan ( x )}

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

p ro v e 2 sin (θ) cos (θ) = sin (2 θ)