# The value of tanθ (θ < 90°) increases as θ increases. Write ‘True’ or ‘False’ and justify your answer

**Solution:**

Given, θ < 90°

We have to determine if the value of tanθ increases as θ increases.

Consider a triangle ABC with perpendicular AC fixed.

So, ABC is a right triangle with C at right angle.

We know that tan A = opposite/adjacent

Here, AC = opposite

tanθ = AC/BC

As θ increases θ₁,

tanθ₁ = AC/B₁C

As θ increases to θ₂,

tanθ₂ = AC/B₂C

We observe that as θ increases to θ₁ and θ₂, BC decreases to B₁C and B₂C.

i.e.,as θ > θ₁ > θ₂ then BC < B₁C < B₂C

Therefore, the value of tanθ increases as θ increases.

**✦ Try This: **Prove that: sin(90° - θ) tanθ = sinθ

We have to prove that sin(90° - θ) tanθ = sinθ

By using trigonometric ratio of complementary angles,

sin(90° - A) = cos A

So, sin(90° - θ) = cos θ

Now, sin(90° - θ) tanθ = cos θ tan θ

We know that tan A = sin A/cos A

So, cos θ tan θ = cos θ (sin θ/cos θ)

= sin θ

Therefore, sin(90° - θ) tanθ = sinθ

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

**NCERT Exemplar Class 10 Maths Exercise 8.2 Sample Problem 2**

## The value of tanθ (θ < 90°) increases as θ increases. Write ‘True’ or ‘False’ and justify your answer

**Summary:**

The tangent function can be expressed as the ratio of the sine function and cosine function.The statement “The value of tanθ (θ < 90°) increases as θ increases” is true

**☛ Related Questions:**

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