Quay lại đáp án

$C=sin^{4}x+sin^{4}(x+\frac{\pi}{4})+sin^{4}(x+\frac{\pi}{2})+sin^{4}(x+\frac{3\pi}{4})$$=sin^{4}x+cos^{4}x+sin^{4}(x+\frac{\pi}{4})+cos^{4}(x+\frac{3\pi}{4}) $$=1-2sin^{2}(x+\frac{\pi}{4})cos^{2}(x+\frac{\pi}{4})+1-2sin^{2}xcos^{2}x$$ =2-\frac{1}{2}sin^{2}(2x+\frac{\pi}{2})-\frac{1}{2}sin^{2}2x $$=2-\frac{1}{2}(cos^{2}2x+sin^{2}2x)$$ =\frac{3}{2}$

$C=sin^{4}x+sin^{4}(x+\frac{\pi}{4})+sin^{4}(x+\frac{\pi}{2})+sin^{4}(x+\frac{3\pi}{4})$$=sin^{4}x+cos^{4}x+sin^{4}(x+\frac{\pi}{4})+cos^{4}(x+\frac{\pi}{4})$$=1-2sin^{2}(x+\frac{\pi}{4})cos^{2}(x+\frac{\pi}{4})+1-2sin^{2}xcos^{2}x$$=2-\frac{1}{2}sin^{2}(2x+\frac{\pi}{2})-\frac{1}{2}sin^{2}2x$$=2-\frac{1}{2}(cos^{2}2x+sin^{2}2x)$$=\frac{3}{2}$