How do you find all solutions for sinx - tanx = 0 where x is between 0 and 2(pi)?

1 Answer
Nghi N. · Kevin B.
Apr 15, 2015

f(x) = sin x - sin x/cos x = sin x*(1 - 1/cos x) = sin x*(cos x - 1)/cos x.
Solve sin x = 0 and (cos x - 1) = 0
Reminder. f(x) undefined when cos x = 0 --> x = pi/2 and (3pi)/2.
sin x = 0 --> x = 0; x = pi; and x = 2pi
cos x - 1 = 0 --> cos x = 1 --> x = 0; and x = 2pi
Answers within period (0, 2pi): 0, pi, 2pi.
Check:
x = pi --> f(x) = 0 - 0 = 0 (correct)

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