# cos θ = (a^{2}+b^{2})/2ab, where a and b are two distinct numbers such that ab > 0. Write ‘True’ or ‘False’ and justify your answer

**Solution:**

Given, a and b are two distinct numbers such that ab > 0.

We have to determine if cos θ = (a² + b²)/2ab

Arithmetic mean > Geometric Mean

As AM = (a + b)/2

GM=**√**ab

So we get

(a² + b²)/2 > **√**a²b²

(a² + b²)/2 > ab

(a² + b²)/2ab > 1

It is given that

cos θ > 1

We know that the value of cos θ varies between 0 and 1.

Base/ Hypotenuse > 1

Base > Hypotenuse

As the value of cos cannot be greater than 1, the given statement is false.

Therefore, the given statement is false.

**✦ Try This: **If 3tan θ = 4 , show that (4 cos θ - sin θ)/(4 cos θ + sin θ) = 1/2.

Given, 3tan θ = 4

We have to prove that (4 cos θ - sin θ)/(4 cos θ + sin θ) = 1/2.

We know that tan A = sin A/cos A

tan θ = 4/3

sin θ = 4

cos θ = 3

So, (4 cos θ - sin θ) = 4(3) - 4 = 12 - 4 = 8

(4 cos θ + sin θ) = 4(3) + 4 = 12 + 4 = 16

Now, (4 cos θ - sin θ)/(4 cos θ + sin θ) = 8/16

= 1/2

Therefore, it is proved that (4 cos θ - sin θ)/(4 cos θ + sin θ) = 1/2.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 8

**NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 10**

## cos θ = (a^{2}+b^{2})/2ab, where a and b are two distinct numbers such that ab > 0. Write ‘True’ or ‘False’ and justify your answer

**Summary:**

The statement “cos θ = (a²+b²)/2ab, where a and b are two distinct numbers such that ab > 0” is false

**☛ Related Questions:**

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