证明 sin(2θ)+cos(2θ)=1

解答

证明

sin (2 θ) + cos (2 θ) = 1

假

求解步骤

sin (2 θ) + cos (2 θ) = 1

两侧不相等

对于

sin (2 θ) + cos (2 θ) = 1

代入

θ = 1

sin (2 \cdot 1) + cos (2 \cdot 1) = 0.49315 \dots

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

整理为小数形式

= 0.49315 \dots

两侧不相等

\Rightarrow 假

p ro v e 25 (sec^{2} (5 x) - tan^{2} (5 x)) = 25

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

p ro v e + \frac{cos ( x )}{1 - sin ( x )} = sec (x) + tan (x)

p ro v e sin (\frac{4 π}{3}) = 3 cos (\frac{2 π}{3})

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