Question

sin (5pi over 4) minus Cos (3 pi over 4)​

Answer 1

Answer:

$sin( \frac{5 \pi}{4} ) - cos( \frac{3 \pi}{4} ) \\ = sin( \pi + \frac{\pi}{4} ) - cos( \pi - \frac{\pi}{4} ) \\ = \{ - sin(\frac{\pi}{4} ) \} - \{ - cos(\frac{\pi}{4} )\} \\ = - sin(\frac{\pi}{4} ) + cos(\frac{\pi}{4} ) \\ = - \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } \\ = 0 \\ \\ reasons: \\ (i) \: sin( \pi + \theta) = - sin(\theta) \\ (ii) \: cos( \pi - \theta) = - cos(\theta)$