If 2x2 cos 60° – 4 cot2 45° – 2 tan 60° = 0, what is the value of x?
(a) 2
(b) 3
(c) √3 – 1
(d) √3 +1
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(d) √3+1
2x2 cos 60° – 4 cot2 45° – 2 tan 60° = 0
⇒ 2x2 x \(\frac12\) – 4 x (1)2 – 2 x √3 = 0
⇒ x2 – 4 – 2√3 = 0 ⇒ x2 = 4 + 2√3
⇒ x2 = 3 + 1 + 2√3 ⇒ x2 = (√3)2 + (1)2 + 2√3
⇒ x2 = (√3 + 1)2 ⇒ x = √3+1.