Question 1180759
first determine if the identify is correct.
i used a calculator with a randomly selected value for x.
the calculator confirmed that the equation is true.


here's my worksheet.


<img src = "http://theo.x10hosting.com/2021/052104.jpg">


step 1 puts the original equation in the worksheet.


step 2 provides the results of dividing both sides of the equation by sec^2(x).


step 3 factors the right side of the eqution by tan^2(x) to make the right side equal to tan^2(x) * (1 + tan^2(x)).


step 4 provide the result of dividing both sides of the eqution by tan^2(x).


step 5 provides the results of converting sec^2(x) to 1/cos^(x) and tan^2(x) to sin^2(x) / cos^2(x).


step 6 provides the results of multiplying both sides of the equation by cos^2(x).


step 7 provides the results of simplifying step 6 by performing the multiplication indicated.


step 8 provides the results of simplifying step 7.


step 9 completes the identity process because sin^2(x) + cos^2(x) = 1.


a reference on basic trig identities is shown below.


you can see that the equation in step 4 is one of those basic identities.


<a href = "https://www.purplemath.com/modules/idents.htm" target = "_blank">https://www.purplemath.com/modules/idents.htm</a>