Question

Find the value of : 4/3 tan 30° + sin^2 60° – 3 cos^2 60° + 3/4 tan^2 60° - 2 tan ^2 45​

Answer 1

Answer:

Hope this will help you...

Answer 2

Given:-

Find the value of 4/3 tan² 30° + sin² 60° - 3 cos² 60° + 3/4 tan² 60° - 2 tan 45°.

Solution:-

$\large\ \frac{4}{3}$ tan² 30° + sin² 60° - 3 cos² 60° + $\large\ \frac{3}{4}$ tan² 60° - 2 tan 45°.

$⇒ \: \: \: \: \frac{4}{3} \: ( \frac{1}{ \sqrt{3}})^{2} \: + (\frac{ \sqrt{3} }{2}^{2}) \: - \: 3( \frac{1}{3})^{2} \: + \frac{3}{4} \: ( \sqrt{3})^{2} \: - \: 2(1)$

$⇒ \: \: \: \: \frac{4}{3} \: × \: \frac{1}{3} \: + \: 3( \frac{1}{4}) \: + \: \frac{3}{4} \: × \: 3 \: - \: 2$

$⇒ \: \: \: \: \frac{4}{9} \: + \: \frac{3}{4} \: - \: \frac{3}{4} \:+ \: \frac{9}{4} \: - \: 2$

$⇒ \: \: \: \: \frac{4}{9} \: + \: \frac{9}{4} \: - \: 2$

$⇒ \: \: \: \frac{4(4) \: + \: 9(9) \: - \: 2(36)}{36}$

$⇒ \: \: \: \frac{16 \: + \: 81 \: - \: 72}{36}$

$⇒ \: \: \: \frac{97 \: - \: 72}{36}$

$⇒ \: \: \: \frac{25}{36}$

∴ Hence, the Answer is $\large\frac{25}{36}$