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受欢迎的三角函数 >

证明 sin(x)(sec(x)tan(x))=tan^2(x)

解答

证明

sin (x) (sec (x) tan (x)) = tan^{2} (x)

解答

真

求解步骤

sin (x) sec (x) tan (x) = tan^{2} (x)

调整左侧

sin (x) sec (x) tan (x)

使用三角恒等式改写

sin (x) sec (x) tan (x)

用 sin, cos 表示

sec (x) sin (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} sin (x)

化简

\frac{1}{cos ( x )} sin (x) : \frac{sin ( x )}{cos ( x )}

\frac{1}{cos ( x )} sin (x)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( x )}{cos ( x )}

乘以:

1 \cdot sin (x) = sin (x)

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )} tan (x)

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x) tan (x)

化简

tan (x) tan (x) : tan^{2} (x)

tan (x) tan (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

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

= tan^{1 + 1} (x)

数字相加:

1 + 1 = 2

= tan^{2} (x)

= tan^{2} (x)

= 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 tan(θ)+cot(θ)= 1/(sin(θ)cos(θ))

p ro v e tan (θ) + cot (θ) = \frac{1}{sin ( θ ) cos ( θ )}

证明 cot^2(x)+csc^2(x)=1+cot^2(x)

p ro v e cot^{2} (x) + csc^{2} (x) = 1 + cot^{2} (x)

证明 tan(B)+cot(B)=csc(B)sec(B)

p ro v e tan (B) + cot (B) = csc (B) sec (B)

证明 4cos(x+y)+4cos(x-y)=8cos(x)cos(y)

p ro v e 4 cos (x + y) + 4 cos (x - y) = 8 cos (x) cos (y)

证明 ((sin(t)+cos(t))^2)/(sin(t)cos(t))=2+sec^2(t)(csc^2(t))

p ro v e \frac{( sin ( t ) + cos ( t ) ) ^{2}}{sin ( t ) cos ( t )} = 2 + sec^{2} (t) (csc^{2} (t))