Kako dokazujete 1 / (1 + sin (theta)) + 1 / (1-sin (theta)) = 2sec ^ 2 (theta)?

Odgovor:

Glej spodaj

Pojasnilo:

LHS = leva stran, RHS = desna stran

LHS# = 1 / (1 + sin theta) + 1 / (1-sin theta) #

# = (1-sin theta + 1 + sin theta) / ((1 + sin theta) (1-sin theta)) #-> Skupni imenovalec

# = (1-preklic v theta + 1 + karkoli v theta) / ((1 + sin theta) (1-sin theta)) #

# = 2 / (1-sin ^ 2x) #

# = 2 / cos ^ 2x #

# = 2 * 1 / cos ^ 2x #

# = 2sec ^ 2x #

# = RHS #