\(\frac{11}{12}\) + cot245° + sin260° + tan230° + sin90° + x = 7, then what should we add in x to make a nearest perfect square?
Answer & explanation
Correct answer: option 2
⇒ \(\frac{11}{12}\) + 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)