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

The solution to (cos(x)+sin(x))^2 is sin(2x)+1

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

simplify

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

sin (2 x) + 1

Solution steps

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

Expand

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

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

Rewrite using trig identities

= sin (2 x) + 1

tan^{2} (x) - 1

\frac{1 + cos ( 2 x )}{2}

sin (x) csc (x)

(5 a + 7 b - 3) + (3 b - 2 a + 9)

(\frac{2}{5})^{2} + \frac{11}{25}