SOLUTION: Simplify: 1 - csc^2 (theta)/cot^2 (theta)

Question 349080: Simplify: 1 - csc^2 (theta)/cot^2 (theta)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(Algebra.com's software will not do theta. So I will use "x" instead.)

When trying to manipulate and simplify expressions with trig functions, it is often helpful to rewrite the expression using only sin and/or cos. The other 4 functions can be written in terms of sin/cos. Using this idea on your expression, and using the facts that csc = 1/sin and cot = cos/sin, we get:

With as the denominator of both "little" fractions, we can simplify this expression by multiplying the numerator and denominator of the "big" fraction by :

On top we will need to use the Distributive Property to multiply:

We know that . So what is ? Answer: !! Substituting this into the expression we get:

The cosines cancel leaving

Your expression simplifies down to -1!
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