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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

The value of 2sinθ can be a+(1/a), where a is a positive number and a≠1. Write ‘True’ or ‘False’ and justify your answer

Solution:

Given, a is positive number and a ≠ 1

We have to determine if 2sinθ can be a + (1/a)

Arithmetic mean of a and 1/a = a + (1/a) / 2

Geometric mean of a and 1/a = √a × (1/a) = 1

So, arithmetic mean > geometric mean

i.e., [a + (1/a)]/2 > 1

[a + (1/a)] > 2

Now, 2sinθ > 2

sinθ > 1

Therefore, 2sinθ cannot be a + (1/a)

✦ Try This: If 5sin A = 3, find cos A

Given, 5sin A = 3

We have to find cos A

sin A = 3/5

We know that sin A = opposite/hypotenuse

By using pythagorean theorem,

(hypotenuse)² = (opposite)² + (adjacent)²

(5)² = (adjacent)² + (3)²

25 = (adjacent)² + 9

(adjacent)² = 25 - 9

(adjacent)² = 16

Taking square root,

adjacent = 4

We know that cos A = adjacent/hypotenuse

cos A = 4/5

Therefore, the value of cos A is 4/5.

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

NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 9

The value of 2sinθ can be a+(1/a), where a is a positive number and a≠1. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “The value of 2sinθ can be a+(1/a), where a is a positive number and a≠1” is false

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