证明 sec(x)-sin^2(x)=cos(x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

sec (1) - sin^{2} (1) = 1.14274 \dots

sec (1) - sin^{2} (1)

整理为小数形式

= 1.14274 \dots

cos (1) = 0.54030 \dots

cos (1)

整理为小数形式

= 0.54030 \dots

两侧不相等

\Rightarrow 假

p ro v e cot^{2} (x) = csc^{2} (x) (1 - sin^{2} (x))

p ro v e \frac{cos ( 2 θ )}{- sin ^{2} ( θ )} = cos^{2} (θ)

p ro v e sin (x) + cot (x) (cos (x)) = csc (x)

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

p ro v e sec (θ) cos (θ) csc (θ) = cot (θ)