Question

Rozwiązać równanie ctgx-tgx=sinx+cosx

Answer 1

a/b - b/a = b/c + a/c

 

a/b - b/a = (b+a)/c |*c

 

ac/b - bc/a = b + a |*a

 

a²c/b - bc = ba + a² |*b

 

a²c - b²c = b²a + a²b

 

c(a²-b²) = a(b²+ab) | /(a²-b²)

 

c = a(b²+ab)/(a²-b²)

 

a =  c(a²-b²)/(b²+ab)

 

a²c - a²b = b²c + b²a

 

a²(c-b) = b²(c+b) |/(c+b)

 

a²(c-b)/(c+b) = b²

 

b = √ a²(c-b)/(c+b)

 

b = a√(c-b)/(c+b)

 

Ave