Question

if cosx=2/5 find the value of cos2x

Answer 1

Solution:

It's given that:

$\rm \longrightarrow \cos(x) = \dfrac{2}{5}$

We have to calculate the value of cos(2x)

We know that:

$\rm \longrightarrow \cos(2x) = \cos^{2} (x) - \sin^{2} (x) =2 \cos ^{2} (x) - 1$

Using this result, we get:

$\rm \longrightarrow \cos(2x) =2 \cos ^{2} (x) - 1$

$\rm \longrightarrow \cos(2x) =2 \times \dfrac{4}{25} - 1$

$\rm \longrightarrow \cos(2x) = \dfrac{8}{25} - 1$

$\rm \longrightarrow \cos(2x) = \dfrac{8 - 25}{25}$

$\rm \longrightarrow \cos(2x) = \dfrac{ - 17}{25}$

★ Therefore, the value of cos(2x) is -17/25 or -0.68.

Answer:

$\rm \hookrightarrow \cos(2x) = \dfrac{ - 17}{25}$

Additional Information:

1. Relationship between sides and T-Ratios.

• sin θ = Height/Hypotenuse
• cos θ = Base/Hypotenuse
• tan θ = Height/Base
• cot θ = Base/Height
• sec θ = Hypotenuse/Base
• cosec θ = Hypotenuse/Height

2. Square formulae.

• sin²θ + cos²θ = 1
• cosec²θ - cot²θ = 1
• sec²θ - tan²θ = 1

3. Reciprocal Relationship.

• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ
• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• tan θ = 1/cot θ

4. Cofunction identities.

• sin(90° - θ) = cos θ
• cos(90° - θ) = sin θ
• cosec(90° - θ) = sec θ
• sec(90° - θ) = cosec θ
• tan(90° - θ) = cot θ
• cot(90° - θ) = tan θ

5. Even odd identities.

• sin -θ = -sin θ
• cos -θ = cos θ
• tan -θ = -tan θ

Answer 2

Given:

cosx=2/5

To Find:

The value of cos2x

Solution:

Trigonometric functions are the functions that define the ratios of the side of the triangle. It shows the relationship between the sides and angles of the triangle. They are also known as circular functions. The trigonometric functions are namely, sine, cosine, tangent, cotangent, secant, cosecant.

The answer to the above question can be used by knowing one of the cosine identities which is,

$cos(2x)=2cos^2x-1$

Now it is given that cosx=2/5, putting the value in the stated value to get the value of the cos(2x),

$cos(2x)=2cos^2x-1\\\\=2*\frac{2^2}{5^2}-1\\\\ =\frac{8}{25}-1\\\\ =\frac{-17}{25}$

Hence, the value of cos(2x) is -17/25.