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受欢迎的三角函数 >

证明 3-sec^2(x)=2-tan^2(x)

解答

证明

3 - sec^{2} (x) = 2 - tan^{2} (x)

解答

真

求解步骤

3 - sec^{2} (x) = 2 - tan^{2} (x)

调整左侧

3 - sec^{2} (x)

使用三角恒等式改写

3 - sec^{2} (x)

使用毕达哥拉斯恒等式:

sec^{2} (x) = tan^{2} (x) + 1

= 3 - (tan^{2} (x) + 1)

化简

3 - (tan^{2} (x) + 1) : - tan^{2} (x) + 2

3 - (tan^{2} (x) + 1)

- (tan^{2} (x) + 1) : - tan^{2} (x) - 1

- (tan^{2} (x) + 1)

打开括号

= - (tan^{2} (x)) - (1)

使用加减运算法则

+ (- a) = - a

= - tan^{2} (x) - 1

= 3 - tan^{2} (x) - 1

化简

3 - tan^{2} (x) - 1 : - tan^{2} (x) + 2

3 - tan^{2} (x) - 1

对同类项分组

= - tan^{2} (x) + 3 - 1

数字相加/相减:

3 - 1 = 2

= - tan^{2} (x) + 2

= - tan^{2} (x) + 2

= - tan^{2} (x) + 2

= - tan^{2} (x) + 2

= 2 - tan^{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 (cot(x)+tan(x))^2=csc^2(x)sec^2(x)

p ro v e (cot (x) + tan (x))^{2} = csc^{2} (x) sec^{2} (x)

证明 cos(3x)=4cos(3x)-3cos(x)

p ro v e cos (3 x) = 4 cos (3 x) - 3 cos (x)

证明 sec^2(a)+csc^2(a)=sec^2(a)csc^2(a)

p ro v e sec^{2} (a) + csc^{2} (a) = sec^{2} (a) csc^{2} (a)

证明 (2sin(x)+cos(x))^2+(2cos(x)-sin(x))^2=5

p ro v e (2 sin (x) + cos (x))^{2} + (2 cos (x) - sin (x))^{2} = 5

证明 cos(a)(sec(a)-cos(a))=sin^2(a)

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