Question

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

Answer 1

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 2

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