\(\frac{11}{12}\) + cot²45° + sin²60° + tan²30° + sin90° + x = 7, then what should we add in x to make a nearest perfect square?

1

⇒ \(\frac{11}{12}\) + cot ² 45° + sin ² 60° + tan ² 30° + sin90° + x = 7

⇒ \(\frac{11}{12}\) + (1)² + (\(\frac{\sqrt {3}}{2}\))² + (\(\frac{1}{\sqrt {3}}\))² + 1 + x = 7

⇒ \(\frac{11}{12}\) + 1 + \(\frac{3}{4}\) + \(\frac{1}{3}\) + 1 + x = 7

⇒ \(\frac{48}{12}\) + x = 7

⇒ x = 7 - 4 

⇒ x = 3

Now, nearest perfect square to 3 is 4. 

so, 3 + 1 (is to be added)