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

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

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

simplify

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

2 cos (a - b) + 2

Solution steps

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

Expand

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

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

Expand

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

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

Use the Pythagorean identity:

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

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

Add the numbers:

1 + 1 = 2

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

Use the Angle Difference identity:

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

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

Factor

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

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

Expand

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

= 2 cos (a - b) + 2

(\frac{3}{2} x - \frac{2}{5}) (2 x - 6)

A (8, - 4) y B (- 2, 4)

(2 e^{- 2 x} - e^{x}) (e^{2 x})

(7^{2 x^{2}})^{- 3 x - 9}

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