The value of sinθ is a+(1/a), where ‘a’ is a positive number. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, a is a positive number.
We have to determine if sin θ is a + (1/a).
Case 1: when a > 1
sin θ = a + (1/a) > 1
Case 2: when a = 1
sin θ = 1 + 1/1 = 2
Case 3: when a < 1
sin θ = a + (1/a) < 1
Therefore, sin θ cannot always be positive.
✦ Try This: If sin θ = b/a then cos θ = ?
Given, sin θ = b/a
We have to find cos θ
We know that sin θ = opposite/hypotenuse
Here, opposite = b
Hypotenuse = a
(hypotenuse)² = (opposite)² + (adjacent)²
a² = b² + (Adjacent)²
(adjacent)² = a² - b²
Taking square root,
adjacent = √(a² - b²)
We know that cos θ = adjacent/hypotenuse
So, cos θ = √(a² - b²)/a
Therefore, cos θ = √(a² - b²)/a
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Sample Problem 4
The value of sinθ is a+(1/a), where ‘a’ is a positive number. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “The value of sinθ is a+(1/a), where ‘a’ is a positive number” is false
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