Identidades trigonométricas del ángulo triple:
sen3x = 3senx-4sen³x
cos3x = 4cos³x-3cosx
Por dato:
nsenx = sen3x
nsenx = 3senx - 4sen³x
4sen³x = (3-n)senx
4sen²x = 3-n
sen²x = (3-n)/4
Piden:
S = cos3x/cosx
S = (4cos³x-3cosx)/cosx
S = 4cos²x-3
Recuerda que
sen²x + cos²x = 1
cos²x = 1 - sen²x
Entonces
S = 4(1 - sen²x) - 3
S = 4(1 - (3-n)/4) -3
S = (4 - (3-n)) - 3
S = (1+n) - 3
S = n - 2
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Identidades trigonométricas del ángulo triple:
sen3x = 3senx-4sen³x
cos3x = 4cos³x-3cosx
Por dato:
nsenx = sen3x
nsenx = 3senx - 4sen³x
4sen³x = (3-n)senx
4sen²x = 3-n
sen²x = (3-n)/4
Piden:
S = cos3x/cosx
S = (4cos³x-3cosx)/cosx
S = 4cos²x-3
Recuerda que
sen²x + cos²x = 1
cos²x = 1 - sen²x
Entonces
S = 4(1 - sen²x) - 3
S = 4(1 - (3-n)/4) -3
S = (4 - (3-n)) - 3
S = (1+n) - 3
S = n - 2