SOLUTION: where x represents the theta prove that sec x(1-sin x)(sec x+tan x) = 1

Question 511681: where x represents the theta
prove that sec x(1-sin x)(sec x+tan x) = 1
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
In this proof you can make use of three identities as follows:
.
which is equivalent to
.

.
and
.
which is equivalent to
.
Start with:
.

.
On the left side replace by its equivalent in two places to get:
.

.
Next replace by its equivalent :
.

.
Multiply the first two terms in parentheses and the equation becomes:
.

.
In the second set of parentheses put everything over the common denominator and this makes the equation become:
.

.
Multiply the two numerators together. Also multiply the two denominators together:
.

.
Now replace the numerator by its equivalent and the equation reduces to:
.

.
Dividing out the left side further reduces the equation to:
.

.
And since the left side has been reduced until it equaled the right side, the proof has been validated. QED (thus it is demonstrated).
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Hope this helps to familiarize you with some of the trig identities and how to use them.
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