Question

Q20.IfsinA=1/2,thenthevalueofcotAis (a)√3. (b)1/√3. (c)√3/2. (d)1​

Answer 1

Trigonometric Ratios

Solving this question requires the knowledge of two simple relations:

1. Python Theorem : To calculate the length of base : The Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

2. Knowledge of basic trigonometric ratios :

• sin(θ) = Perpendicular/Hypotenuse
• cot(θ) = Base/Hypotenuse.

Given that,

$\sin(A) = \dfrac{1}{2} = \dfrac{Perpendicular}{Hypotenuse} = \dfrac{P}{H}$

We know that,

$\boxed{\bm{H^2 = P^2 + B^2}}$

By substituting the known values in the formula, we get:

$\implies 2^2 = 1^2 + B^2 \\ \\ \implies 4 = 1 + B \\ \\ \implies B^2 = 4 - 1 \\ \\ \implies B^2 = 3 \\ \\ \implies B = \sqrt{3}$

Now, the value of cot(A) will be;

We know that,

$\boxed{\bm{\cot(A) = \dfrac{Base}{Perpendicular} = \dfrac{B}{P}}}$

By substituting the known values in the formula, we get:

$\implies \cot(A) = \dfrac{\sqrt{3}}{1} \\ \\ \implies \cot(A) = \sqrt{3}$

Hence, the value of cot(A) is √3. So option (a) is correct.

$\rule{90mm}{2pt}$

MORE TO KNOW

1. Relationship between sides and T-Ratios.

• sin(θ) = Height/Hypotenuse
• cos(θ) = Base/Hypotenuse
• tan(θ) = Height/Base
• cot(θ) = Base/Height
• sec(θ) = Hypotenuse/Base
• cosec(θ) = Hypotenuse/Height

2. Square formulae.

• sin²(θ) + cos²(θ) = 1
• 1 + tan²(θ) = sec²(θ)
• 1 + cot²(θ) = cosec²(θ)

3. Reciprocal Relationship.

• sin(θ) = 1/cosec(θ)
• cos(θ) = 1/sec(θ)
• tan(θ) = 1/cot(θ)
• cot(θ) = 1/tan(θ)
• sin(θ)/cos(θ) = 1/cot(θ)
• cos(θ)/sin(θ) = 1/tan(θ)
• sin2(θ) = 2sin(θ)cos(θ)
• cos2(θ) = cos²(θ) - sin²(θ)

Answer 2

Answer:

Option (a) √3

Step-by-step explanation:

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