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Blackshadesidn

2 sin A = √3

=》sin A = √3/2

■ If sin A = √3/2, then A = 60° (trigonometric value)

So,

cot A = cot 60° = 1/√3

1 - cot²A / 2 cot A

= 1 - (1/√3)² / 2*(1/√3)

= 1 - (1/3) / 2/√3

= 2/3 / 2/√3

= 2/3 / 2√3/3

Cancel out the 3 in the denominator.

= 2/2√3

= 1/√3

1 - cot²A / 2 cot A = 1/√3

_____

● See the attachment for the trigonometric values.

Hope it helps ⚜

View image Blackshades
Mhanifaidn

Answer:

  • √3/3

Step-by-step explanation:

  • 2 sinA = √3 ⇒ sinA = √3/2

Rewrite as:

  • (1 - cot²A)/2cotA =
  • (1 - cos²A/sin²A)/(2cosA/sinA) =
  • sinA[(sin²A - cos²A)/sin²A] / (2cosA) =
  • (2sin²A - 1)/(2sinAcosA) =
  • (2sin²A - 1)/[2sinA√(1 - sin²A)]

Substitute the value of sinA:

  • (2(√3/2)² - 1) / [√3 √{1 - (√3/2)²)] =
  • (3/2 - 1)/[√3√(1/4)] =
  • (1/2) /(√3/2) =
  • 1/√3 =
  • √3/3
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