The value of 4 cot2 45° – sec260º + sin2 60° + cos2 90° is
(a) \(\frac12\)
(b) \(\frac34\)
(c) 1
(d) \(\frac{11}{16}\)
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(b) \(\frac34\)
4 cot2 45° – sec2 60° + sin2 60° + cos2 90°
= 4 (cot 45°)2 – (sec 60°)2 + (sin 60°)2 + (cos 90°)2
= 4 × 12 – (2)2 + \(\bigg(\frac{\sqrt3}{2}\bigg)\) + (0)2
= 4 – 4 + \(\frac34\) + 0 = \(\frac34\).