Question 1206383
<pre>
i)

{{{cot^""(x) - cot^""(2x)}}}{{{""=""}}}{{{cosec(2x^"")}}}

{{{cos^""(x)/sin^""(x)-cos^""(2x)/sin^""(2x)}}}

{{{cos^""(x)/sin^""(x)-(cos^2(x)-sin^2(x))/(2sin^""(x)cos^""(x))}}}

{{{expr((2cos^""(x))/(2cos^""(x)))*expr( (cos^""(x))/(sin^""(x)))-(cos^2(x)-sin^2(x))/(2sin^""(x)cos^""(x))}}}

{{{(2cos^2(x))/(2sin^""(x)cos^""(x))-(cos^2(x)-sin^2(x))/(2sin^""(x)cos^""(x))}}}

{{{(2cos^2(x)-(cos^2(x)-sin^2(x)))/(2sin^""(x)cos^""(x))}}}

{{{(2cos^2(x)-cos^2(x)+sin^2(x))/(2sin^""(x)cos^""(x))}}}

{{{(cos^2(x)+sin^2(x))/(2sin^""(x)cos^""(x))}}}

{{{1^""/(2sin^""(x)cos^""(x))}}}

Change the denominator back to sin(2x)

{{{1^""/sin^""(2x)}}}

{{{cosec(2x^"")}}}

Edwin</pre>