prove that:
[tex] {sin}^{2} \: \frac{7\pi}{8} + \: {sin}^{2} \: \frac{5\pi}{8} = 1 [/tex]

Question

contestada

$prove thattex sin2 frac7pi8 sin2 frac5pi8 1 tex class=$

Respuesta :

LammettHash LammettHash · Answer 1 · 2021-01-01T06:42:17+01:00

Recall that

sin²(x) = (1 - cos(2x))/2

so that

sin²(7π/8) = (1 - cos(7π/4))/2

sin²(5π/8) = (1 - cos(5π/4))/2

Then

sin²(7π/8) + sin²(5π/8) = (1 - cos(7π/4) + 1 - cos(5π/4))/2

… = 1 - 1/2 (cos(7π/4) + cos(5π/4))

… = 1 - 1/2 (1/√2 - 1/√2)

… = 1

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