证明 25sin^2(x)+25cos^2(x)=25

解答

证明

25 sin^{2} (x) + 25 cos^{2} (x) = 25

真

求解步骤

25 sin^{2} (x) + 25 cos^{2} (x) = 25

调整左侧

25 sin^{2} (x) + 25 cos^{2} (x)

使用三角恒等式改写

25 sin^{2} (x) + 25 cos^{2} (x)

使用毕达哥拉斯恒等式:

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

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

= 25 (1 - cos^{2} (x)) + 25 cos^{2} (x)

25 (1 - cos^{2} (x)) + 25 cos^{2} (x) = 25

25 (1 - cos^{2} (x)) + 25 cos^{2} (x)

乘开

25 (1 - cos^{2} (x)) : 25 - 25 cos^{2} (x)

25 (1 - cos^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 25, b = 1, c = cos^{2} (x)

= 25 \cdot 1 - 25 cos^{2} (x)

数字相乘:

25 \cdot 1 = 25

= 25 - 25 cos^{2} (x)

= 25 - 25 cos^{2} (x) + 25 cos^{2} (x)

p ro v e cot (x) sin (x) sec (x) = 1

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

p ro v e tan^{2} (t) = \frac{1}{cos ^{2} ( t )} - 1

p ro v e \frac{cot ( θ ) - tan ( θ )}{cot ( θ ) + tan ( θ )} = cos (2 θ)

p ro v e cos^{2} (2 x) + 4 sin^{2} (x) cos^{2} (x) = 1