cidyah has taken the correct approach. His answer is correct with one exception. Your solution set can only contain values of x for which the expression on the left and right are defined. The number p/2 is not in the domain of the expression on the right. It can not be included in the solution set.

sec(x) - tan(x) = cos(x)

1/cos(x) - sin(x)/cos(x) = cos(x) ==> 1 - sin(x) = cos²(x)

with the restriction that cos(x) ? 0. Use the ID cos²(x) = 1 - sin²(x):

1 - sin(x) = 1 - sin²(x) ==> sin²(x) - sin(x) = 0 ==> sin(x)[sin(x) - 1] = 0

So either sin(x) = 0, or 1 - sin(x) = 0.

sin(x) = 0 if x = 0, p, 2p, ..., kp where k is any integer.

sin(x) = 1 if x = p/2, 5p/2, ..., p/2 + 2pk for any integer k.

However, the latter values are not in the domain of either the secant or the tangent. So these are not in the solution set. The complete solution set can be expressed as

{x | x = kp, k any integer}.

**** Update ****

Beware! Every respondent that includes 90° or p/2 is in error!

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