What is (cos(x)+cos(y))^2+(sin(x)+sin(y))^2 ?

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

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simplify (cos(x)+cos(y))^2+(sin(x)+sin(y))^2

simplify

(cos (x) + cos (y))^{2} + (sin (x) + sin (y))^{2}

2 cos (x - y) + 2

Solution steps

(cos (x) + cos (y))^{2} + (sin (x) + sin (y))^{2}

Expand

(cos (x) + cos (y))^{2} : cos^{2} (x) + 2 cos (x) cos (y) + cos^{2} (y)

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

Expand

(sin (x) + sin (y))^{2} : sin^{2} (x) + 2 sin (x) sin (y) + sin^{2} (y)

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

Use the Pythagorean identity:

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

= 2 cos (x) cos (y) + 2 sin (x) sin (y) + 1 + 1

Add the numbers:

1 + 1 = 2

= 2 cos (x) cos (y) + 2 sin (x) sin (y) + 2

Use the Angle Difference identity:

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

= 2 (1 + cos (x - y))

Factor

2 cos (x) cos (y) + 2 sin (x) sin (y) + 2 : 2 (cos (x) cos (y) + sin (x) sin (y) + 1)

= 2 (cos (x - y) + 1)

Expand

2 (cos (x - y) + 1) : 2 cos (x - y) + 2

= 2 cos (x - y) + 2

sec (b) (cos (b) + sin (b))

(- 3, 5) y (- 4, - 1)

\frac{( 2 x + 4 )}{s ( s ^{2} + 5 )}

sin (y) (e^{x} + e^{x} y)

x y + (2 x^{2} + 3 y^{2} - 20) \frac{d y}{d x}

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