Question 1099175
Given that θ is an acute​ angle, rewrite csc(θ-45°) an equivalent value using its cofunction.
<pre>
I don't think you meant "cofunction" since the cofunction of the 
cosecant is the secant.  There are no formulas directly connecting
the secant to the cosecant, so I think you mean "reciprocal", which
is the sine, not the "cofunction".  So I'll do it using the reciprocal, 
since I know of no way to simplify the expression using the secant.

{{{csc(theta-"45°")}}}{{{""=""}}}

{{{1^""/sin(theta-"45°")^""}}}{{{""=""}}}

{{{1^""/(sin(theta)cos("45°")-cos(theta)sin("45°"))}}}{{{""=""}}}

{{{1^""/(sin(theta)(sqrt(2)/2)-cos(theta)(sqrt(2)/2)^"")}}}{{{""=""}}}

Simplify by multiplying numerator and denominator through by 2

{{{2^""/(sin(theta)(sqrt(2))^""-cos(theta)(sqrt(2)))}}}{{{""=""}}}

Factor out {{{sqrt(2)}}} in the bottom:

{{{2^""/(sqrt(2)(sin(theta)^""-cos(theta)))}}}{{{""=""}}}

Multiply numerator and denominator by {{{sqrt(2)}}}

{{{2^""sqrt(2)/(sqrt(2)sqrt(2)(sin(theta)^""-cos(theta)))}}}{{{""=""}}}

{{{2^""sqrt(2)/(2(sin(theta)^""-cos(theta)))}}}{{{""=""}}}

{{{cross(2)^""sqrt(2)/(cross(2)(sin(theta)^""-cos(theta)))}}}{{{""=""}}}

{{{sqrt(2)^""/(sin(theta)^""-cos(theta))}}}

Edwin</pre>