Question

$evaluate \: {sin}^{2} \frac{2\pi}{3} + {cos}^{2} \frac{5\pi}{6} - {tan}^{2} \frac{3\pi}{4}$


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Answer 1

we have

$\sf { sin^{2} \big ( \frac{2 \pi}{3} \big ) + cos^{2} \big( \frac{5 \pi}{6} \big ) - tan^{2} \big ( \frac{3 \pi}{4} \big )}$

$\sf{ = sin^{2} (\pi - \frac{ \pi}{3}) + cos^{2} ( \pi - \frac{ \pi}{6} ) - tan^{2} ( \pi - \frac{ \pi}{4} ) }$

$\large\sf { = \frac{ \sqrt{3}}{2}^{2} + \frac{ \sqrt{3}}{2}^{2} - 1}$

$\large\sf{ = \frac{3}{4} + \frac{3}{4} -1}$

$\large\sf{ = \frac{3}{2} - 1}$

$\large\sf { \therefore \frac{1}{2}}$ is the required answer.