What is (sin(a)+cos(a))^2+(sin(a)-cos(a))^2 ?

The solution to (sin(a)+cos(a))^2+(sin(a)-cos(a))^2 is 2

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

simplify

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

2

Solution steps

(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)

Simplify

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)

Rewrite using trig identities

= 2

- (\frac{3}{2})^{2}

4 \cdot (- a^{2})

45 \cdot 7

4 x^{12}

\frac{2 x ^{4}}{4}

What is (sin(a)+cos(a))^2+(sin(a)-cos(a))^2 ?
The solution to (sin(a)+cos(a))^2+(sin(a)-cos(a))^2 is 2