Question

Si cotx - cscx=√9
Calcula 9(cotx + cscx)

Answer 1

cot(x) tan(x) = 1 
cot^2(x) tan(x) = cot(x) 

Entonces 

tan(x) + cot(x) + cot(x) = sec(x) csc(x) + (4/3) 

tan(x) + 2 cot(x) = sec(x) csc(x) + (4/3) 


Multiplicamos todo por sen(x) cos(x) 

sen^2(x) + 2 cos^2(x) = 1 + (4/3) sen(x) cos(x) 

sen^2(x) + cos^2(x) + cos^2(x) = 1 + (4/3) sen(x) cos(x) 

1 + cos^2(x) = 1 + (4/3) sen(x) cos(x) 

cos^2(x) = (4/3) sen(x) cos(x) 

cos(x) = (4/3) sen(x) 

cot(x) = cos(x)/sen(x) = 4/3 
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E = √[ 9 *(cot^2(x) + 1) ] 

E = √[ 9 *((4/3)^2 + 1) ] 

E = √[ 9 *((16/9) + 1) ] 

E = √[ 16 + 9] 

E = √[25] 

E = 5 
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