Question

how to verify

cot(x)sec^4(x) equals cot(x)+2tan(x)+tan^3(x)

Answer 1

2tan(x) is the correct term? cause I am getting 2tan^2(x)

Answer 2

yes 2tan(x) is the correct term

Answer 3

\[\cot(x) * \sec^4(x) = \cot(x) * (\sec^2(x))^2\]
\[\cot(x) * \sec^4(x) = \cot(x) * (\tan^2(x) +1)^2\]
\[\cot(x) * \sec^4(x) = \cot(x) * ((\tan^2(x))^2 +1 + 2\tan^2(x))\]
\[\cot(x) * \sec^4(x) = \cot(x) * (\tan^4(x)) +\cot(x) + 2\cot(x)*\tan^2(x))\]
\[\cot(x) * \sec^4(x) = \tan^3(x) +\cot(x) + 2\tan(x))\]