If a = 45° and b = 15°, what is the value of ?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 2)
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  1. 2 - 2√2 
  2. 3 - √6 
  3. 3 - √2
  4. 2 - √3

Answer (Detailed Solution Below)

Option 4 : 2 - √3
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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Given:

a = 45° and b = 15

Concept used:

a2 - b2 = (a + b)(a - b)

(a - b)2 = a2 - 2ab + b2

Calculation:

(a - b) = 45° - 15° = 30°

(a + b) = 45° + 15° = 60°

Now, 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 2 - √3

∴ The simplified value is 2 - √3.

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