Question

verify: cot(x)+tan(x)=sec(x)*csc(x)

Answer 1

\[ctg(x) + \tan(x) = \sec(x)*\csc(x)\]
\[we know that : ctg(x) = \frac{ \cos(x) }{ sen(x) } and \tan(x) = \frac{ sen(x) }{\cos(x) }\]
so
\[\frac{ sen(x) }{ \cos(x) } + \frac{ \cos(x) }{ sen(x) } = \sec(x) * \csc(x)\]
\[\frac{ sen^2(x) + \cos^2(x) }{ \cos(x)*sen(x) } = \sec(x) * \csc(x)\]
but, we know sen^2(x) + cos^2(x) = 1
\[\frac{ 1 }{sen(x)*\cos(x) } = \sec(x)*\csc(x)\]
\[\frac{ 1 }{ sen(x) } * \frac{ 1 }{ \cos(x) } = Sec(x) * Csc(x)\]
\[Sec(x) * Csc(x) = Sec(x) * Csc(x)\]

Answer 2

thnxxxx i get it