Question

sec A (1 - sin A) (sec A + tan A) = 1.​

Answer 1

Answer:

LHS = Sec A (1 - Sin A) (Sec A + tan A)

      = (Sec A - Sec A.Sin A) (Sec A + tan A)

      = Sec A - 1/cos A.Sin A (Sec A + tan A)

      = (Sec A - tan A) (Sec A + tan A)

      = Sec²A - tan²A                                       [(a+b)(a-b)=a²-b²]

      = 1

RHS = 1

LHS = RHS

Therefore, Sec A(1 - sin A) (sec A + tan A) = 1