SOLUTION: cosecant theta + cotangent theta * cosecant theta

SOLUTION: cosecant theta + cotangent theta * cosecant theta - cotangent theta = 1

Question 223721: cosecant theta + cotangent theta * cosecant theta - cotangent theta = 1
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(Algebra'com's formula software doesn't "do" theta's for some reason. So I will use t instead.)
Since this problem doesn't work out very well as you've written it, I going to assume that there are supposed to be parentheses:

If this is wrong, stop reading.

When you don't see a better way to solve a problem in Trig., it is often helpful to rewrite the expressions in terms of sin and cos. So we will be replacing csc(t) with 1/sin(t) and cot(t) with cos(t)/sin(t):

To multiply this it helps if you recognize that it fits the pattern: with "a" being 1/sin(t) and "b" being cos(t)/sin(t). Using this pattern (or multiplying out the long way with FOIL and combining like terms) we get:

which simplifies to:

The fractions have the same denominator so we can subtract them:

Since the numerator becomes:

And the fraction cancels leaving

And with this final equation, since 1 always equal 1, shows that your original equation is also always true. We call this an identity.
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