Question 1140527

Show that 
(a) (sec^4-1)/(tan^2x) =2tan^2x 
(b) (cosec^4x -1)/(cot^2x) =2+cot^2x
(c) (1+sec@)/(sin@+tan@)=cosec@
(d) (cos^3@-sin^2@)/(cos@-sin@)=1+sin@cos@
(e) (1-(sin@-cos@)^2/sin@=2cos@
<pre>(a) should be: {{{matrix(1,3, (sec^4 (x) - 1)/tan^2 (x), "=", highlight(tan^2 (x) + 2))}}}
<b><u>We'll focus on the left-side:</b></u> {{{matrix(5,3, (sec^4 (x) - 1)/tan^2 (x), "=", highlight(tan^2 (x) + 2), (sec^2 (x) - 1)(sec^2 (x) + 1)/tan^2 (x), "=", highlight(tan^2 (x) + 2), tan^2 (x)(tan^2 (x) + 1 + 1)/tan^2 (x), "=", highlight(tan^2 (x) + 2), cross(tan^2 (x))(tan^2 (x) + 2)/cross(tan^2 (x)), "=", highlight(tan^2 (x) + 2), highlight(tan^2 (x) + 2), "=", highlight(tan^2 (x) + 2))}}}