证明 2sin^2(2x)+cos(4x)=1

解答

证明

2 sin^{2} (2 x) + cos (4 x) = 1

真

求解步骤

2 sin^{2} (2 x) + cos (4 x) = 1

调整左侧

2 sin^{2} (2 x) + cos (4 x)

使用三角恒等式改写

2 sin^{2} (2 x) + cos (4 x)

使用倍角公式:

1 - 2 sin^{2} (x) = cos (2 x)

- 2 sin^{2} (x) = cos (2 x) - 1

= cos (4 x) - (cos (2 \cdot 2 x) - 1)

cos (4 x) - (cos (2 \cdot 2 x) - 1) = 1

cos (4 x) - (cos (2 \cdot 2 x) - 1)

数字相乘:

2 \cdot 2 = 4

= cos (4 x) - (cos (4 x) - 1)

- (cos (4 x) - 1) : - cos (4 x) + 1

- (cos (4 x) - 1)

打开括号

= - (cos (4 x)) - (- 1)

使用加减运算法则

- (- a) = a, - (a) = - a

= - cos (4 x) + 1

= cos (4 x) - cos (4 x) + 1

p ro v e cos (α - β) - cos (α + β) = 2 sin (α) sin (β)

p ro v e 1 = sec^{2} (θ) - tan^{2} (θ)

p ro v e tan^{8} (x) = tan^{6} (x) sec^{2} (x) - tan^{6} (x)

p ro v e 2 (sin (2 y) cos (2 y)) = sin (4 y)

p ro v e \frac{( tan ^{2} ( t ) )}{sec ( t )} = sec (t) - cos (t)