Answer (Detailed Solution Below)

Option 1 : 1 + √2
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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Concept:

  • cos 2A = cos2 A – sin2 A = 1 – 2 sin2 A = 2 cos2 A – 1


Calculation:

As we know that, cot x = cos x / sin x

As we know that, 

As we know that, 0° < A / 2 < 90° where all trigonometric ratios are positive.

      -------(1)

As we know that, 

      -------(2)

As we know that, 0° < A / 2 < 90° where all trigonometric ratio’s are positive.

So, from equation (1) and (2), we get

Rationalization above the equation

       (∵ a2 - b2 = (a + b)(a - b)

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