7. Evaluate: (4 / Cot² 30°) + (1 / sin² 60° ) - cos² 45°

1.	7. Evaluate: (4 / Cot² 30°) + (1 / sin² 60° ) - cos² 45°
Answer» Step-by-step EXPLANATION: We KNOW that, $\cot(30) = \sqrt{3}$ $\sin(60) = \frac{ \sqrt{3} }{2}$ $\cos(45) = \frac{1}{2}$ The QUESTION, $\frac{4}{ \cot(30) \times \cot(30) } + \frac{1}{ \sin(60) \times \sin(60) } - ( \cos(45) \times \cos(45) )$ $= \frac{4}{ { \sqrt{3} }^{2} } + \frac{1}{ { (\frac{ \sqrt{3} }{2} )}^{2} } - { \frac{1}{2} }^{2}$ $= \frac{4}{3} + \frac{4}{3} - \frac{1}{4}$ $= \frac{29}{12}$

Answer»

Step-by-step EXPLANATION:

We KNOW that,

$\cot(30) = \sqrt{3}$