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

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

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

expand

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

sin (2 \cdot \frac{1}{x}) + 1

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= sin (2 \cdot \frac{1}{x}) + 1

(- 1 + i)^{9}

(- x y + \frac{5}{8}) (\frac{3}{4} - x y)

(2 x + 12) \cdot (- 0.5)

(2 + 3 y + y^{2})^{5}

(8 x + 5 y) cos (5 y) + sin (8 x + 5 y) sin (5 y)

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