Simplify the expression cos^2 x (sec^2 x-1)
Note that cosx*secx = 1
so (cosx*secx)^2 = 1 also.
Your expression is therefore
1 - cos^2x = sin^2x
To simplify the expression cos^2 x (sec^2 x-1), let's break down each component and simplify them individually.
1. Start with the expression sec^2 x - 1:
The trigonometric identity sec^2 x - 1 is equal to tan^2 x. So we can replace sec^2 x - 1 with tan^2 x.
2. Now, the expression becomes cos^2 x * tan^2 x.
3. Next, use the trigonometric identity tan^2 x = sin^2 x / cos^2 x:
Substitute tan^2 x with sin^2 x / cos^2 x.
4. Rearrange the expression:
Now, we have cos^2 x * (sin^2 x / cos^2 x).
5. Simplify:
The cos^2 x cancels out with one of the cos^2 x terms in the numerator and denominator, leaving us with sin^2 x.
Therefore, the simplified form of the expression cos^2 x (sec^2 x-1) is sin^2 x.