Question

Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer. 7 sin^2(x) sec^2(x) - 7 sin^2(x)

Answer 1

To factor and simplify the expression, start by factoring out the common factor of sin^2(x), then simplify using the fundamental identity.

Step-by-step explanation:

To factor the expression and use the fundamental identities to simplify, we can start by factoring out the common factor of sin^2(x) from both terms:

7 sin^2(x) sec^2(x) - 7 sin^2(x)

= 7 sin^2(x) (sec^2(x) - 1)

Next, we can simplify sec^2(x) - 1 using the fundamental identity sec^2(x) - 1 = tan^2(x):

= 7 sin^2(x) tan^2(x)

So, the simplified expression is 7 sin^2(x) tan^2(x).