证明 tan^2(x)+2=sec^2(x)+1

解答

证明

tan^{2} (x) + 2 = sec^{2} (x) + 1

真

求解步骤

tan^{2} (x) + 2 = sec^{2} (x) + 1

调整右侧

sec^{2} (x) + 1

使用三角恒等式改写

sec^{2} (x) + 1

使用毕达哥拉斯恒等式:

sec^{2} (x) = tan^{2} (x) + 1

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

化简

= tan^{2} (x) + 2

= tan^{2} (x) + 2

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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

p ro v e 8 sin^{2} (θ) + 9 cos^{2} (θ) = 8 + cos^{2} (θ)

p ro v e sec^{2} (x) + tan^{2} (x) = 1 + 2 tan^{2} (x)

p ro v e cot (x + π) = cot (x)

p ro v e tan (x) (2 - cos (x))^{2} = 0