Question

1) If Sin 0 - Cos 0 = 0, then what of (Sin⁴∅ + Cos⁴∅?​

Answer 1

$if \: \: \: sin \theta - cos \theta = 0 \\ \: \: \: sin \theta = cos \theta \\ tan \theta = 1 \\ \theta = \frac{\pi}{4} \\ \\ \\ {sin}^{4} \theta + {cos}^{4} \theta \\ = {sin}^{4} \frac{\pi}{4} + {cos}^{4} \frac{\pi}{4} \\ = ( { \frac{1}{ \sqrt{2} } })^{4} + ( { \frac{1}{ \sqrt{2} } })^{4} \\ = \frac{1}{4} + \frac{1}{4} \\ = \frac{1}{2}$