Menjawab:
Silakan lihat buktinya di bawah ini
Penjelasan:
Kita butuh
# sectheta = 1 / costheta #
# sin ^ 2theta + cos ^ 2theta = 1 #
Oleh karena itu
# LHS = (sectheta-1) / (sectheta + 1) #
# = (1 / costheta-1) / (1 / costheta + 1) #
# = (1-costheta) / (1 + costheta) #
# = ((1-costheta) (1 + costheta)) / ((1 + costheta) (1 + costheta)) #
# = (1-cos ^ 2theta) / (1 + costheta) ^ 2 #
# sin ^ 2theta / (1 + costheta) ^ 2 #
# = (sintheta / (1 + costheta)) ^ 2 #
# = RHS #
# QED #
# LHS = (secx-1) / (secx + 1) #
# = (1 / cosx-1) / (1 / cosx + 1) #
# = (1-cosx) / (1 + cosx) * (1 + cosx) / (1 + cosx) #
# = (1-cos ^ 2x) / (1 + cosx) ^ 2 = sin ^ 2x / (1 + cosx) ^ 2 = (sinx / (1 + cosx)) ^ 2 = RHS #
Menjawab:
Penjelasan di bawah ini
Penjelasan:
# (secx-1) / (secx + 1) #
=# ((secx-1) * (secx + 1)) / (secx + 1) ^ 2 #
=# ((secx) ^ 2-1) / (secx + 1) ^ 2 #
=# (tanx) ^ 2 / (secx + 1) ^ 2 #
=# (sinx / cosx) ^ 2 / (1 / cosx + 1) ^ 2 #
=# ((sinx) ^ 2 / (cosx) ^ 2) / ((1 + cosx) ^ 2 / (cosx) ^ 2) #
=# (sinx) ^ 2 // (1 + cosx) ^ 2 #
=# (sinx / (1 + cosx)) ^ 2 #
