Eton Commercial School (Tel: 6245 8494)

Given
sec A + tan A = 1, evaluate sin A

Solution

sec A + tan A = 1
1/cosA + sinA/cosA = 1
1+sinA = cosA (multiplying cosA both sides)
(1+sinA)^2 = cos^2A (square both sides)
1 + 2sinA + sin^2A = cos^2A
1 + 2sinA + sinA^2 = (1-sin^2A) (using trigo identity, sin^2A + cos^2A = 1)
2sin^2A + 2sinA = 0
sinA(sinA + 1) = 0

sinA = 0, sinA = -1