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If tan2x° = cot(x+6)°, then find the value of x?

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If tan2x° = cot(x+6)°, then find the value of x?
1. 44° 
2. 25° 
3. 38° 
4. 28° 
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Correct Answer - Option 4 : 28° 

Given:

 tan2x° = cot(x+6)°

Concept used:

tan(90° - θ) = cotθ 

Calculation:

 tan2x° = cot(x+6)°

⇒  tan2x° = tan[90° - (x+6)°]                           [tan(90° - θ) = cotθ]

⇒ 2x° = 90° - (x+6)°

⇒ 2x° = 90° - x° - 6° 

⇒ 3x° = 84° 

⇒ x = 28° 

∴ The value of x is 28°.

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