证明 (sin(x))(tan(x)cos(x)-cot(x)cos(x))=1-2cos(2x)

解答

证明

(sin (x)) (tan (x) cos (x) - cot (x) cos (x)) = 1 - 2 cos (2 x)

假

求解步骤

sin (x) (tan (x) cos (x) - cot (x) cos (x)) = 1 - 2 cos (2 x)

两侧不相等

对于

sin (x) (tan (x) cos (x) - cot (x) cos (x)) = 1 - 2 cos (2 x)

代入

x = 1

sin (1) (tan (1) cos (1) - cot (1) cos (1)) = 0.41614 \dots

sin (1) (tan (1) cos (1) - cot (1) cos (1))

整理为小数形式

= 0.41614 \dots

1 - 2 cos (2 \cdot 1) = 1.83229 \dots

1 - 2 cos (2 \cdot 1)

整理为小数形式

= 1.83229 \dots

两侧不相等

\Rightarrow 假

p ro v e sin (2 0^{\circ}) = 2 cos (1 0^{\circ}) \cdot sin (1 0^{\circ})

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

p ro v e 1 - 2 sin^{2} (2 θ) = 8 cos^{4} (θ) - 8 cos^{2} (θ) + 1

p ro v e sech^{2} (x) + tanh^{2} (x) = 1

p ro v e 2 cos^{2} (A) - cos (2 A) - 1 = 0