SOLUTION: Given that θ is an acute​ angle, rewrite csc(θ-45°) an equivalent value using its cofunction.

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Question 1099175: Given that θ is an acute​ angle, rewrite csc(θ-45°) an equivalent value using its cofunction.
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
Given that θ is an acute​ angle, rewrite csc(θ-45°) an equivalent value using its cofunction.
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%28theta-%2245%B0%22%29%22%22=%22%22

1%5E%22%22%2Fsin%28theta-%2245%B0%22%29%5E%22%22%22%22=%22%22

1%5E%22%22%2F%28sin%28theta%29cos%28%2245%B0%22%29-cos%28theta%29sin%28%2245%B0%22%29%29%22%22=%22%22

%22%22=%22%22

Simplify by multiplying numerator and denominator through by 2

2%5E%22%22%2F%28sin%28theta%29%28sqrt%282%29%29%5E%22%22-cos%28theta%29%28sqrt%282%29%29%29%22%22=%22%22

Factor out sqrt%282%29 in the bottom:

2%5E%22%22%2F%28sqrt%282%29%28sin%28theta%29%5E%22%22-cos%28theta%29%29%29%22%22=%22%22

Multiply numerator and denominator by sqrt%282%29

%22%22=%22%22

2%5E%22%22sqrt%282%29%2F%282%28sin%28theta%29%5E%22%22-cos%28theta%29%29%29%22%22=%22%22

%22%22=%22%22

sqrt%282%29%5E%22%22%2F%28sin%28theta%29%5E%22%22-cos%28theta%29%29

Edwin