Question

What number should be subtracted from

4(sin⁴60° + cos⁴30°) - (tan²45° - cot²30°) + cos²45° - cosec²45°+ sec²60° to get 2 ?

1. 5
2. 4
3. 7
4. 3

Answer 1

Correct Answer - Option 3 : 7

Calculations:

4[√3/2)⁴ + (√3/2)⁴] - 1 + (√3)² + (1/√2)² - (√2)² + (2)²

⇒ 4[(9/16) + (9/16)] - 1 + 3 + (1/2) - 2 + 4

⇒ (9/2) - 1 + 3 + (1/2) + 2

⇒ 5 + 5 - 1

⇒ 9

Now let the number be x that must be subtracted to get 2 

⇒ 9 - x = 2 

⇒ x = 7

∴ The correct choice will be option 3.