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

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

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

simplify

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

2 sin (a + b) + 2

Solution steps

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

Expand

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

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

Expand

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

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

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= 2 cos (a) sin (b) + 2 cos (b) sin (a) + 1 + 1

Add the numbers:

1 + 1 = 2

= 2 cos (a) sin (b) + 2 cos (b) sin (a) + 2

Use the Angle Sum identity:

sin (s) cos (t) + cos (s) sin (t) = sin (s + t)

= 2 (1 + sin (a + b))

Factor

2 cos (a) sin (b) + 2 cos (b) sin (a) + 2 : 2 (cos (a) sin (b) + cos (b) sin (a) + 1)

= 2 (sin (a + b) + 1)

Expand

2 (sin (a + b) + 1) : 2 sin (a + b) + 2

= 2 sin (a + b) + 2

(tan (x) + 1) (3 cot (x) - 1)

- \frac{7 ( 3 + 5 2 )}{41} - 2 - 32

t^{2} μ (t - 1) + t cos (5 t)

(y + \frac{1}{3})^{2}

(x^{2} - 1) x

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