Question

someone please help me.
Verify the identity. Justify each step. tan θ + cot θ = 1/ sin θcos θ

Answer 1

\[\tan x+\cot x=\frac{ \sin x }{ \cos x }+\frac{ \cos x }{ \sin x }\]
\[=(\frac{ \sin x }{ \cos x })(\frac{ \sin x }{ \sin x }+(\frac{ sinx }{ \cos x })(\frac{ \cos x }{ \cos x })\]
\[=(\frac{ (\sin x)^{2} }{ sinx \cos x })+(\frac{ (\cos x)^{2} }{ sinx \cos x })\]
\[=\frac{ ((sinx)^{2}+(\cos x)^{2} )}{ sinx \cos x}\]
\[=\frac{ 1 }{ sinx cosx }\]

Answer 2

thanks :)