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

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

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

expand

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

sin (2 ln (x)) + 1

Solution steps

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

Apply Perfect Square Formula:

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

a = cos (ln (x)), b = sin (ln (x))

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

Use the Pythagorean identity:

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

= 2 cos (ln (x)) sin (ln (x)) + 1

Use the Double Angle identity:

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

= sin (2 ln (x)) + 1

(1 - \frac{1 - cos ( x π )}{2}) 1 0^{\frac{x}{2}}

\frac{1}{8} e^{4 x} (- 4 e^{- 4 t} t - e^{- 4 t})

2 cos (5) (2 tan (5) x + 25)

y^{2} d x + (x^{2} + x y) d y

sin (θ) - cos (θ) (sin (θ) - cos (θ))

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