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

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

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

expand

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

sin (2 ln (x)) + 1

Solution steps

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

Apply Perfect Square Formula:

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

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

= sin^{2} (ln (x)) + 2 sin (ln (x)) cos (ln (x)) + cos^{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 + i)^{7}

(1 + i)^{6}

(2 x - y) (2 x + 3 y)

\frac{x + 3}{x ( x + 17 )}

x^{2} + y^{2} \times (x^{2} + y^{2})

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