The value of the expression (cos2 23° - sin2 67°) is positive. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, the expression is cos² 23° - sin² 67°
We have to determine if (cos² 23° - sin² 67°) is positive.
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
Now, cos² 23° - sin² 67° = (cos 23° - sin 67°)(cos 23° + sin 67°)
By using trigonometric ratio of complementary angles,
sin (90° - A) = cos A
sin 67°= sin(90°- 23°) = cos 23°
cos² 23° - sin² 67° = (cos23° - cos23°)(cos23° + cos23°)
= (0)(2cos23°)
= 0
Therefore, cos² 23° - sin² 67° = 0
✦ Try This: The value of the expression (cosec² 23° - sec² 67°) is
Given, the expression is cosec² 23° - sec² 67°
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
So, cosec² 23° - sec² 67° = (cosec 23° + sec 67°)(cosec 23° - sec 67°)
By using trigonometric ratios of complementary angles,
cosec (90° - A) = sec A
So, cosec 23° = cosec(90° - 67°) = sec 67°
Now, cosec² 23° - sec² 67° = (sec 67° + sec 67°)(sec 67° - sec 67°)
= (2sec 67°)(0)
= 0
Therefore, cosec² 23° - sec² 67° = 0
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 2
The value of the expression (cos2 23° - sin2 67°) is positive. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “the value of the expression (cos² 23° - sin² 67°) is positive” is false. As cos² 23° - sin² 67° = 0 which is neither positive nor negative
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