- Question: sin(x)cos(x)(1 + tan2(x)) =
(a) tan(x) + 1
(b) cos(x)
(c) sin(x)
(d) tan(x)
(e) sin(x) + cos(x)
Answer: sin(x)cos(x)(1 + tan2(x)) =sin(x)cos(x)(1 + sin2(x)/cos2(x)) =sin(x)cos(x)[(cos2(x) + sin2(x))/cos2(x)] =
sin(x)cos(x)[1/cos2(x)] = sin(x)/cos(x) = tan(x)
- Question: For any x such that 0 < x < ¶/2, the expression (1 - sin2x)/cos(x) + (1 – cos2x)/sin(x) is equivalent to:
(a) sin(x)
(b) cos(x)
(c) sin(x) – cos(x)
(d) sin(x) + cos(x)
(e) 2sin(x)Answer:
(1 – sin2x)/cos(x) + (1 – cos2x)/sin(x) = cos2x/cos(x) +
sin2x/sin(x) = sin(x) + cos(x).
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