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If , 6(sec59° - cot31°] + 2/3 × sin 90° - 3 × tan56° ×  y × tan34° = y/3 then the value of y is:
1. 2
2. 3
3. 1
4. 4

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Correct Answer - Option 1 : 2

Given: 

 6(sec59° - cot31°] + 2/3 × sin 90° - 3 × tan56° ×  y × tan34° = y/3 

Formulas used:

cosec(90°- A) = sec A

tan(90° - A) = cot A 

cosec2A- cot2 A = 1

Calculation:

6(sec59° - cot31°] + 2/3 × sin 90° - 3 × tan56° ×  y × tan34° = y/3  

⇒ 6[sec2(90°- 31°) - cot2 31°] + 2/3 × 1 - 3 × tan2(90°- 34°) × y × tan234° = y/3 

⇒6[cosec231°- cot2 31°] + 2/3 - 3 × cot234°× y × tan234° = y/3 

⇒ 6 × 1 + 2/3 - 3 × 1/tan234°× tan234° × y = y/3

⇒ 6 + 2/3 - 3y = y/3 

⇒ 20/3 = y/3 + 3y 

⇒ 20/3 = 10y/3 

⇒ 20 = 10y 

∴ y = 2 

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