If 2sin(3x -15)° = 1, 0° < (3x - 15) < 90°, then find the value of cos2(2x +15)° + cot2 (x + 15)°.

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SSC CGL 2020 Tier-I Official Paper 5 (Held On : 16 Aug 2021 Shift 2)
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SSC CGL Tier 1 2025 Full Test - 01
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Given:

2sin(3x -15)° = 1

Calculation:

sin(3x - 15)° = 1/2

⇒ sin (3x - 15)° = sin 30° 

⇒ (3x - 15)° = 30° 

⇒ 3x = 30° + 15° = 45° 

⇒ x =  = 15° 

Then,

cos2(2x +15)° + cot(x +15)°

cos2(2 × 15 +15)° + cot(15 +15)°

⇒ cos2(45)° + cot2(30)°

⇒  + 

⇒  + 3 =  

∴ cos2(2x +15)° + cot(x +15)° = 

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