3. [0.5/1 Points] Verify the identity. (Simplify your answers completely.) 2sec^6(x)(sec(x)tan(x))-2sec^4(x)(sec(x)tan(x))=2sec^5(x)tan^3(x) 2sec^5(x)[sec[x][cot(x)]=2sec^4(x)[sec[x]tan[x]]=2sec^2[x](sec(x)(tan]x)[square

## Step 1<br />The problem involves verifying the identity of a trigonometric equation. The equation given is \(2sec^{6}(x)(sec(x)tan(x))-2sec^{4}(x)(sec(x)tan(x))=2sec^{5}(x)tan^{3}(x)\).<br /><br />## Step 2<br />The first step is to simplify the left side of the equation. We can do this by factoring out the common terms.<br /><br />### \(2sec^{6}(x)(sec(x)tan(x))-2sec^{4}(x)(sec(x)tan(x)) = 2sec^{4}(x)(sec(x)tan(x))(sec^{2}(x)-1)\)<br /><br />## Step 3<br />Next, we simplify the right side of the equation.<br /><br />### \(2sec^{5}(x)tan^{3}(x) = 2sec^{4}(x)(sec(x)tan(x))(sec(x)tan^{2}(x))\)<br /><br />## Step 4<br />Now, we compare the simplified left side and right side of the equation.<br /><br />### \(2sec^{4}(x)(sec(x)tan(x))(sec^{2}(x)-1) = 2sec^{4}(x)(sec(x)tan(x))(sec(x)tan^{2}(x))\)<br /><br />## Step 5<br />Finally, we simplify the right side of the equation.<br /><br />### \(2sec^{4}(x)(sec(x)tan(x))(sec(x)tan^{2}(x)) = 2sec^{5}(x)tan^{3}(x)\)