Question

Suppose Cosine (x) = StartFraction 1 Over StartRoot 5 EndRoot EndFraction and sin(x) > 0. What is the value of tan(2x)? NOWw

Answer 1

Answer:

C. 4/3

Step-by-step explanation:

Answer 2

The value of tan(2x) is -4/3

What is double angle formula for tan?

Let, 'm' be an angle then the double angle formula of tan is,

$tan(2m)=\frac{2~tan(m)}{1-tan^{2}m }$

For given example,

We have cos(x) = 1/√5 and sin(x) > 0

We know, sin^2(x) + cos^(x) = 1

⇒ sin^2(x) = 1 - (1/√5)^2

⇒ sin^2(x) = 1 - (1/5)

⇒ sin^2(x) = 4/5

⇒ sin(x) = ± 2/√5

But sin(X) > 0

⇒ sin(x) = 2/√5

We know, for any angle Ф,

tan(Ф) = sin(Ф) / cos(Ф)

Hence, tan(x) = sin(x)/cos(x)

tan(x) = (2/√5) / (1/√5)

⇒ tan(x) = 2/1

⇒ tan(x) = 2

Now, using the double angle formula for tan,

$\Rightarrow tan(2x)=\frac{2~tan(x)}{1-tan^{2}x }\\\\\Rightarrow tan(2x)=\frac{2\times 2}{1-(2)^{2}}\\\\ \Rightarrow tan(2x)=\frac{4}{1-4}\\\\ \Rightarrow \bold{tan(2x)=-\frac{4}{3}}$

Therefore, the value of tan(2x) is -4/3

Learn more about the double angle here:

https://brainly.com/question/15385122

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