Antwoord:
Zie het onderstaande bewijs
Uitleg:
Wij hebben nodig
# Sectheta = 1 / costheta #
# Sin ^ 2 theta + cos ^ 2teta = 1 #
Daarom, de
# 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 ^ 2 theta) / (1 + costheta) ^ 2 #
# Sin ^ 2teta / (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 ^ 2 x / (1 + cosx) ^ 2 = (sinx / (1 + cosx)) ^ 2 = RHS #
Antwoord:
Uitleg hieronder
Uitleg:
# (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 #
