What is expand (1+sin(θ)+cos(θ))^2 ?

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

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expand (1+sin(θ)+cos(θ))^2

expand

(1 + sin (θ) + cos (θ))^{2}

2 cos (θ) + 2 sin (θ) + sin (2 θ) + 2

Solution steps

(1 + sin (θ) + cos (θ))^{2}

Apply exponent rule:

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

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

= (1 + sin (θ) + cos (θ)) (1 + sin (θ) + cos (θ))

Distribute parentheses

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

Simplify

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

= 2 cos (θ) + 2 sin (θ) + sin (2 θ) + 2

(2 + 1 + x)^{2}

(x^{2} + 3 x + 2) (5 x + 9 x^{2} - 2 x)

(\frac{1}{x} - 1) (\frac{1}{x} + 1)

(4 - 4 cos (θ))^{2}

(e^{ia} - e^{- ia}) (e^{ib} + e^{- ib})

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