Consider the following numbers :
I. tan 22.5°
II. cot 22.5°
III. tan 22.5° - cot 22.5°
How many of the above are irrational numbers?

Question

Question

This question was previously asked in

NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)

Answer 1

Explanation:

(I) Let tan 22.5° = tan 45/2 = t

⇒ tan45° =

=

⇒ 1 = ⇒ t² + 2t –1 = 0

⇒ t =

⇒ tan (In first quadrant tan is positive}

This is an irrational number.

(II) cot22.5° =

This is also an irrational number

(III) tan22.5° – cot22.5° = -1+ √2 -(1 +√ 2)

= -2

This is not an irrational number

∴ Option (c) is correct.

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