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On [0, pi/2], f = sin x and g = cos x. f + g takes the value 1 at

Ax = 0 and x = pi/2
Bx = pi/4 only
Cx = pi/6 and pi/3
Dx = pi/3 only
Answer & Solution
Correct answer: A. x = 0 and x = pi/2
At x = 0, sin + cos = 0 + 1 and at x = pi/2 it is 1 + 0, so f + g repeats a value and is not one-one.
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