Question

If sin A = 1/2, then the value of cot A is
(A) √3
(B) 1/√3
(C) √3/2
(D) 1​

Answer 1

Given :-

• sinA = 1/2

We need to find :-

• cotA = ?

Solution :-

♦ Method 1 :-

First finding cosA using first trigonometric identity

• sin²A + cos²A = 1

By simplifying ,

• cosA = ± √1 - sin²A

Substituting the value of sinA

➸ cosA = ± √ 1 - [ 1/2 ]²

➸ cosA = ± √ 1 - 1²/2²

➸ cosA = ± √ 1 - 1/4

➸ cosA = ± √ 3/4

➸ cosA = √3/√4

➸ cosA = √3/2

Now finding cotA

• cotA = cosA/sinA

➮ cotA = [ √3 / 2 ]/ [ 1/2 ]

➮ cotA = √3/1

➮ cotA = √3

♦ Method 2 :-

sinA = 1/2

Substituting ,

Substituting 1/2 = sin30°

• sinA = sin30°

By comparing

• A = 30°

Now substituting the value of A in cotA

→ cotA

→ cot30°

→ cotA = √3

Hence , cotA = √3 . So option (A) is your answer

Answer 2

$\bf \sf \implies \huge \{question \}$

If sin A = 1/2, then the value of cot A is

Given

• SinA = 1/2
• So P =1 and B =2

Find

• Cot A= ?

Formula used

H^2 = B^2 +P^2

$\bf \large \pink solution$

$\bf \ { H }^{2} = { \: P\: }^{2} + { B }^{2}$

${2}^{2} = {1}^{2} + { B }^{2}$

$B = \sqrt{3}$

Now we know that

cot A = B/P

so Cot A = √3

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