Question

solo la g y h
demostrar las siguientes identidades​

Answer 1

Recuerda:

$\sin(2x) = 2 \sin(x) \cos(x)$

$\cos(2x) = \cos {}^{2} (x) - \sin {}^{2} (x)$

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

g)

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

h)

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