化简 (sin(a)+cos(a))^2+(sin(a)-cos(a))^2

解答

化简

(sin (a) + cos (a))^{2} + (sin (a) - cos (a))^{2}

2

求解步骤

(sin (a) + cos (a))^{2} + (sin (a) - cos (a))^{2}

(- cos (a) + sin (a))^{2} : cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a)

= cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a) + (cos (a) + sin (a))^{2}

(cos (a) + sin (a))^{2} : cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a)

= cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a) + cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a)

化简

cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a) + cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) : 2 cos^{2} (a) + 2 sin^{2} (a)

= 2 cos^{2} (a) + 2 sin^{2} (a)

使用三角恒等式改写

= 2

s im pl i f y - (\frac{3}{2})^{2}

s im pl i f y 4 \cdot (- a^{2})

s im pl i f y 45 \cdot 7

s im pl i f y \frac{2 x ^{4}}{4}

s im pl i f y c^{4} \cdot c^{3}