Question

2 sin square 30 tan 60 + 3cos square 60 sec square 30​

Answer 1

Answer:

I attached a picture for step by step explanation

Answer 2

SOLUTION

TO EVALUATE

2 sin² 30° tan 60° + 3 cos² 60° sec² 30°

EVALUATION

Here the given expression is

2 sin² 30° tan 60° + 3 cos² 60° sec² 30°

We find the value as below

2 sin² 30° tan 60° + 3 cos² 60° sec² 30°

$\displaystyle \sf{ = 2 \times { \bigg( \frac{1}{2} \bigg)}^{2} \times \sqrt{3} + 3 \times { \bigg( \frac{1}{2} \bigg)}^{2} \times { \bigg( \frac{ \sqrt{3} }{2} \bigg)}^{2}}$

$\displaystyle \sf{ = 2 \times \frac{1}{4} \times \sqrt{3} + 3 \times \frac{1}{4} \times \frac{3}{4} }$

$\displaystyle \sf{ = \frac{ \sqrt{3} }{2} + \frac{9}{16} }$

$\displaystyle \sf{ = \frac{9 + 8 \sqrt{3} }{16} }$

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