Exercise\left(sec x + sin^2x + cos^2x\right)\left(sec x - 1\right)
Step-by-step Solution
1
Math interpretation of the question
$\left(x\sec\left(x\right)+\sin\left(x\right)^{2x}+\cos\left(x\right)^{2x}\right)\left(\sec\left(x\right)-1\right)$
2
Multiply the single term $\sec\left(x\right)-1$ by each term of the polynomial $\left(x\sec\left(x\right)+\sin\left(x\right)^{2x}+\cos\left(x\right)^{2x}\right)$
$x\sec\left(x\right)\left(\sec\left(x\right)-1\right)+\sin\left(x\right)^{2x}\left(\sec\left(x\right)-1\right)+\cos\left(x\right)^{2x}\left(\sec\left(x\right)-1\right)$
Intermediate steps
3
Multiply the single term $x\sec\left(x\right)$ by each term of the polynomial $\left(\sec\left(x\right)-1\right)$
$x\sec\left(x\right)^2-x\sec\left(x\right)+\sin\left(x\right)^{2x}\left(\sec\left(x\right)-1\right)+\cos\left(x\right)^{2x}\left(\sec\left(x\right)-1\right)$
Explain this step further
4
Multiply the single term $\sin\left(x\right)^{2x}$ by each term of the polynomial $\left(\sec\left(x\right)-1\right)$
$x\sec\left(x\right)^2-x\sec\left(x\right)+\sec\left(x\right)\sin\left(x\right)^{2x}-\sin\left(x\right)^{2x}+\cos\left(x\right)^{2x}\left(\sec\left(x\right)-1\right)$
5
Multiply the single term $\cos\left(x\right)^{2x}$ by each term of the polynomial $\left(\sec\left(x\right)-1\right)$
$x\sec\left(x\right)^2-x\sec\left(x\right)+\sec\left(x\right)\sin\left(x\right)^{2x}-\sin\left(x\right)^{2x}+\sec\left(x\right)\cos\left(x\right)^{2x}-\cos\left(x\right)^{2x}$
Final answer to the exercise $x\sec\left(x\right)^2-x\sec\left(x\right)+\sec\left(x\right)\sin\left(x\right)^{2x}-\sin\left(x\right)^{2x}+\sec\left(x\right)\cos\left(x\right)^{2x}-\cos\left(x\right)^{2x}$