Question

express cos(sec-cos) in terms of sin

Answer 1

\(\LARGE\color{blue}{ \bf cos~x~(sec~x~-cos~x) = }\) expand and you get,

\(\LARGE\color{blue}{ \bf 1~-cos^{2}~x }\)

then use the rule
\[Sin^{2}x+Cos^{2}x=1~~~~~~~that~~~gives~~~~~ 1-\cos^{2}x=\sin^{2}x\]