证明 cos(x)sec(x)+tan(x)=1+sin(x)

解答

证明

cos (x) sec (x) + tan (x) = 1 + sin (x)

假

求解步骤

cos (x) sec (x) + tan (x) = 1 + sin (x)

两侧不相等

对于

cos (x) sec (x) + tan (x) = 1 + sin (x)

代入

x = 1

cos (1) sec (1) + tan (1) = 2.55740 \dots

cos (1) sec (1) + tan (1)

整理为小数形式

= 2.55740 \dots

1 + sin (1) = 1.84147 \dots

1 + sin (1)

整理为小数形式

= 1.84147 \dots

两侧不相等

\Rightarrow 假

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

p ro v e 1 - sin^{5} (x) = cos^{2} (x)

p ro v e cot (\frac{π}{2} - θ) cot (θ) = 1

p ro v e \frac{csc ^{2} ( t )}{cot ( t )} = tan (t) + cot (t)

p ro v e 4 (5 cos (2 x)) + (- 20 cos (2 x)) = 0