What is expand (1+sin(x)+cos(x))^2 ?

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

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expand (1+sin(x)+cos(x))^2

expand

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

2 cos (x) + 2 sin (x) + sin (2 x) + 2

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Distribute parentheses

= 1 \cdot 1 + 1 \cdot sin (x) + 1 \cdot cos (x) + sin (x) \cdot 1 + sin (x) sin (x) + sin (x) cos (x) + cos (x) \cdot 1 + cos (x) sin (x) + cos (x) cos (x)

Simplify

1 \cdot 1 + 1 \cdot sin (x) + 1 \cdot cos (x) + sin (x) \cdot 1 + sin (x) sin (x) + sin (x) cos (x) + cos (x) \cdot 1 + cos (x) sin (x) + cos (x) cos (x) : 2 cos (x) + 2 sin (x) + sin (2 x) + 2

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

\frac{1}{( a x + b ) ( a x - 2 b )}

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

cot (θ) (\frac{1}{3 cos ( θ )} + tan (θ))

1 - cos (x) (1 + cos (x))

cos (2 x) (sec (2 x) - 1)

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