证明 sin(2x)-cos(2x)=1-2cos(2x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

sin (2 \cdot 1) - cos (2 \cdot 1) = 1.32544 \dots

sin (2 \cdot 1) - cos (2 \cdot 1)

整理为小数形式

= 1.32544 \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 tan (x) (csc^{(2)} (x) - 1) = cot (x)

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

p ro v e csc (x) tan (x) = \frac{1}{cos ( x )}

p ro v e sin (x + y) sin (x - y) = sin (2 x) - sin (2 y)

p ro v e sin (\frac{5 π}{6}) = \frac{1}{2}