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
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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