PreCalc
posted by Jess .
How do I solve this? My work has led me to a dead end.
tan(45x) + cot(45x) =4
my work:
(tan45  tanx)/(1+ tan45tanx) + (cot45  cotx)/(1 + cot45cotx) = 4
(1tanx)/(1+tanx) + (1cotx)/(1+cotx) = 4
Then I found a common denominator, giving me this:
(22cotxtanx)/(1+cotx+tanx+cotxtanx) =4
I can't cancel the cotxtanx's because they're in the middle of a term, right? So where do I go from here? Or did I make a mistake somewhere?
This is how I would soleve it. First put 45  x = y. Then:
Sin(y)/Cos(y) + Cos(y)/Sin(y) = 4 >
[Sin^2(y) + Cos^2(y)]/(Sin(y)Cos(y)) = 4
1/(Sin(y)Cos(y)) = 4 >
Sin(2y) = 1/2
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