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受欢迎的三角函数 >

证明 (6cos^2(x)-6sin^2(x))=6-12sin^2(x)

解答

证明

(6 cos^{2} (x) - 6 sin^{2} (x)) = 6 - 12 sin^{2} (x)

解答

真

求解步骤

6 cos^{2} (x) - 6 sin^{2} (x) = 6 - 12 sin^{2} (x)

调整左侧

6 cos^{2} (x) - 6 sin^{2} (x)

使用三角恒等式改写

6 cos^{2} (x) - 6 sin^{2} (x)

使用毕达哥拉斯恒等式:

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

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

= 6 (1 - sin^{2} (x)) - 6 sin^{2} (x)

化简

6 (1 - sin^{2} (x)) - 6 sin^{2} (x) : 6 - 12 sin^{2} (x)

6 (1 - sin^{2} (x)) - 6 sin^{2} (x)

乘开

6 (1 - sin^{2} (x)) : 6 - 6 sin^{2} (x)

6 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 6, b = 1, c = sin^{2} (x)

= 6 \cdot 1 - 6 sin^{2} (x)

数字相乘:

6 \cdot 1 = 6

= 6 - 6 sin^{2} (x)

= 6 - 6 sin^{2} (x) - 6 sin^{2} (x)

同类项相加:

- 6 sin^{2} (x) - 6 sin^{2} (x) = - 12 sin^{2} (x)

= 6 - 12 sin^{2} (x)

= 6 - 12 sin^{2} (x)

= 6 - 12 sin^{2} (x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

流行的例子

证明 1+1/(tan^2(x))=csc^2(x)

p ro v e 1 + \frac{1}{tan ^{2} ( x )} = csc^{2} (x)

证明 sec(x*0)=1

p ro v e sec (x \cdot 0) = 1

证明 (1+csc(a))/(cot(a)+cos(a))=sec(a)

p ro v e \frac{1 + csc ( a )}{cot ( a ) + cos ( a )} = sec (a)

证明 sec(θ)-sec(θ)sin^2(θ)=cos(θ)

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

证明 2cos(2x)=4cos^2(x)-2

p ro v e 2 cos (2 x) = 4 cos^{2} (x) - 2