What is expand (sin(6x)+cos(6x))^2 ?

The solution to expand (sin(6x)+cos(6x))^2 is sin(2*6x)+1

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expand (sin(6x)+cos(6x))^2

expand

(sin (6 x) + cos (6 x))^{2}

sin (2 \cdot 6 x) + 1

Solution steps

(sin (6 x) + cos (6 x))^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(sin (6 x) + cos (6 x))^{2} = sin^{2} (6 x) + 2 sin (6 x) cos (6 x) + cos^{2} (6 x)

= sin^{2} (6 x) + 2 sin (6 x) cos (6 x) + cos^{2} (6 x)

Simplify

sin^{2} (6 x) + 2 sin (6 x) cos (6 x) + cos^{2} (6 x) : sin (2 \cdot 6 x) + 1

= sin (2 \cdot 6 x) + 1

sin (θ) + (sin (θ) + cos (θ)) cos (θ)

- cos (x) \cdot 6 (2 x + 1)^{2}

(e^{0.5 x} - 2)^{2}

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

8 x e^{- 0.4 x} + 8 (x - 7.556) e^{- 0.4 (x - 7.556)}

What is expand (sin(6x)+cos(6x))^2 ?
The solution to expand (sin(6x)+cos(6x))^2 is sin(2*6x)+1