If sin A = 1/2 , then the value of cot A is
a. √3
b. 1/√3
c. √3/2
d. 1

Solution:

Given, sin A = 1/2

We have to find the value of cot A.

We know that sin A = opposite / hypotenuse

Opposite = 1

Hypotenuse = 2

Using the pythagorean theorem,

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

(2)² = (adjacent)² + (1)²

4 = (adjacent)² + 1

(adjacent)² = 4 - 1

(adjacent)² = 3

Taking square root,

Adjacent = √3

We know that cot A = adjacent / opposite

Cot A = √3/1

Therefore, the value of cot A is √3.

✦ Try This: If tan B = 3/4, then the value of cot B is

Given, tan B = 3/4

We have to find the value of cot B

We know that tan B = opposite/adjacent

Opposite = 3

Adjacent = 4

We know that cot B = adjacent/opposite

Cot B = 4/3

Therefore, the value of cot B is 4/3.

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

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NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 2

If sin A = 1/2 , then the value of cot A is a. √3, b. 1/√3, c. √3/2, d. 1

Summary:

The cotangent of an angle in a right triangle is defined as the ratio of the adjacent side (the side adjacent to the angle) to the opposite side (the side opposite to the angle). If sin A = 1/2 , then the value of cot A is √3

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☛ Related Questions:

• The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is a. . . . .
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