Cos^2x-sin^2x/sin^2x+sinxcosx=cotx- 1

Step-by-step explanation:

We're going to start by manipulating the left side of the equation and making it the same form as .

Start by applying the difference of two squares formula to the numerator, like so:

Now simplify the denominator by expanding the .

The denominator can even be further simplified since both addends (when added together = a sum) have the common factor of . Factor it out.

Cancel out the common factor .

Since this is the furthest simplified that the left side can be manipulated, let's see if can try to manipulate the right side to also look like .

Start by expressing with and , since we know that cotangent is simply .

We can simplify this expression to look like our expression we found by manipulating the left side by making the 1 have a common denominator of .

To do this, multiply 1 by . Now the expression should look like:

Since they have a common denominator we can write the expression under one fraction, like so:

This looks exactly the same as what we manipulated the left side to be , just without parentheses. I put both expressions in bold. Therefore, this identity proves to be true as we just proved it.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

answer:   y=2x-3

step-by-step explanation: