If √3 tan θ = 1, then find the value of sin² θ - cos² θ

Solution:

It is given that

√3 tan θ = 1

It can be written as

tan θ = 1/√3

By taking tan inverse

θ = tan^-1 (1/√3)

θ = 30°

To determine the value of sin² θ - cos² θ

Let us substitute the value of θ

sin² 30° - cos² 30°

= (1/2)² - (√3/2)²

By further simplification

= 1/4 - 3/4

So we get

= -2/4 

= -1/2

Therefore, the value of sin² θ - cos² θ is -1/2.

✦ Try This: Show that tan⁴ θ +tan² θ = sec⁴ θ - sec² θ.

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

NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 9

If √3 tan θ = 1, then find the value of sin² θ - cos² θ

Summary:

Basic trigonometry formulas are used to find the relationship of trigonometric ratios and the ratio of the corresponding sides of a right-angled triangle. If √3 tan θ = 1, then the value of sin² θ - cos² θ is -1/2

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