Question

evaluate:

(4/tan^2 60 + 1/cos^2 30 - 2sin^2 45) / (sin^2 60 +
cos^2 45)     {ans 4/3} 

Answer 1

$tan(60^o) = \sqrt{3} \\ \\ tan^2(60^o) = 3 \\ \\ cos(30^o) = \frac{ \sqrt{3} }{2} \\ \\ cos^2(30^o) = \frac{3}{4} \\ \\ sin(45^o) = cos(45^o) = \frac{1}{ \sqrt{2} } \\ \\ sin^2(45^o) = cos^2(45^o) = \frac{1}{2} \\ \\ sin(60^o) = \frac{ \sqrt{3} }{2} \\ \\ sin^2(30^o) = \frac{3}{4}$

Now substitute the values

$\frac{ \frac{4}{(3)} + \frac{1}{( \frac{3}{4} )} - \frac{2}{ (\frac{1}{2} )} }{( \frac{3}{4} ) + ( \frac{1}{4} )} \\ \\ \frac{4}{3} + \frac{4}{3} - 4 \\ \\ \frac{8}{3} - 4 \\ \\ -\frac{4}{3}$

Answer 2

Step-by-step explanation:

I hope it will be helpful to you