The value of the expression (sin 80° - cos 80°) is negative. Write ‘True’ or ‘False’ and justify your answer

Solution:

Given, the expression is sin 80° - cos 80°

We have to determine if the expression is negative.

θ	0°	30°	45°	60°	90°
sinθ	0	1/2	1/√2	√3/2	1
cosθ	1	√3/2	1/√2	1/2	0

From the trigonometric ratio of angles,

sin θ increases as θ increases from 0° to 90°

cos θ decreases as θ increases from 0° to 90°

So, (sin 80° - cos 80°) = (increasing value - decreasing value)

= positive value

Therefore, (sin 80° - cos 80°) > 0

✦ Try This: The value of the expression (cos 60° - sin 30°) is

Given, the expression is cos 60° - sin 30°

From the trigonometric ratio of angles,

cos 60° = 1/2

sin 30° = 1/2

So, cos 60° - sin 30° = 1/2 - 1/2

= 0

Therefore, cos 60° - sin 30° = 0

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

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NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 3

The value of the expression (sin 80° - cos 80°) is negative. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “The value of the expression (sin 80° - cos 80°) is negative” is false as the solution of the expression is greater than zero which is positive

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