Question

sec(–α)cosαcotα

Answer 1

\[\sec(-\alpha)=\frac{1}{\cos(-\alpha)}=\frac{1}{\cos\alpha}=\sec\alpha\]
\[\sec(-\alpha)\cos\alpha\cot\alpha=\sec\alpha\cos\alpha\cot\alpha=\cot\alpha\]
since \(\sec\alpha\cos\alpha=\dfrac{\cos\alpha}{\cos\alpha}=1\).

Answer 2

\(\large\color{darkblue}{ \rm sec(-α)cos(α)cot(α) }\)
\(\large\color{darkblue}{ \rm sec(α)cos(α)cot(α) }\)
\(\large\color{darkblue}{ \rm (1/cos~α)~cos(α)~~cot(α) }\)
\(\large\color{darkblue}{ \rm cot(α) }\)