Question

Evaluate 5 sin^2 30° + cos^2 45° - 4 tan^2 30° / 2 sin 30°cos 30° + tan 45°

Answer 1

Step-by-step explanation:

In this question, we need to evaluate the following expression i.e.

$\dfrac{5\sin^230+\cos^245-4\tan^2 30}{2\sin30\cos30+\tan45}$

The values of following trigonometric quantities are:

$\sin30=\dfrac{1}{2}\\\\\cos45=\dfrac{1}{\sqrt2}\\\\\tan 30=\dfrac{1}{\sqrt 3}\\\\\cos30=\dfrac{\sqrt3}{2}\\\\\tan45=1$

So,

$=\dfrac{5\times (\dfrac{1}{2})^2+(\dfrac{1}{\sqrt2})^2-4\times (\dfrac{1}{\sqrt3})^2}{2\times \dfrac{1}{2}\times \dfrac{\sqrt3}{2}+1}\\\\=\dfrac{\dfrac{5}{4}+\dfrac{1}{2}-\dfrac{4}{3}}{\dfrac{\sqrt3}{2}+1}\\\\=\dfrac{5}{6(\sqrt 3+2)}$

Hence, this is the required solution.  

Answer 2

Answer:

Please refer to the attachment .

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