SOLUTION: Please I need help!! Does this verify as an identity???? How would you solve this?? sec^4 x tan^2 x = (tan^2x + tan^4 x) sec^2 x

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Question 1180759: Please I need help!!
Does this verify as an identity???? How would you solve this??
sec^4 x tan^2 x = (tan^2x + tan^4 x) sec^2 x
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


...use "Pythagorean" identity:1+%2B+tan%5E2%28+x%29=sec%5E2%28+x%29
sec%5E4+%28x%29+%2Atan%5E2%28+x%29+=+tan%5E2%28x%29%2Asec%5E2%28+x%29%2Asec%5E2%28+x%29
sec%5E4+%28x%29+%2Atan%5E2%28+x%29+=+tan%5E2%28x%29%2Asec%5E4%28+x%29-> identity proven

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.



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.

https://www.purplemath.com/modules/idents.htm