These appear to be identities.
Memorize these important definitions:
A.
 = \frac {sin(x)}{cos(x)})
B.
 = \frac {1}{sin(x)})
C.
 = \frac {1}{cos(x)})
Also, remember this important identity:
D.
 + cos^2(x) = 1)
Here's the first problem as you wrote it.
} + sec(x) = \frac {cos(x)}{sin(x)} + 1)
1. using items (A), you'd get:
}{cos(x)}} + sec(x) = \frac {cos(x)}{sin(x)} + 1)
and
}{sin(x)} + sec(x) = \frac {cos(x)}{sin(x)} + 1)
This would only be true if
 = 1)
, but that's not possible for all x. I believe you entere the problem incorrectly.
For the others, do the same substitutions. Try to manipulate the equations so that what you see on the left is the same as the right. This is how you prove identities.
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