identity

cscx-cotx*cosx=sinx A few transformations we can make based on trig identities: csc(x) = 1/sin(x) cot(x) = cos(x)/sin(x) So we have: 1/sin(x) - cos(x)/sin(x) * cos(x) = sin(x) (1 - cos^2(x))/sin(x) = sin(x) 1 - cos^2(x) = sin^2(x) This is true from the identity: sin^2(x) - cos^2(x) = 1

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b We have a logarithmic property that states: ln(a) - ln(b) = ln (a / b) We're given a < b, so (a / b) < 1 Therefore: ln (a / b) < 0 And since ln(a) - ln(b) = ln (a / b) Then Ln(a) - Ln(b) < 0 Add Ln(b) to...

if Logb(5)=3.56 and logb(8)=4.61 then what is logb(40) There exists a logarithmic identity which says log(xy) = log(x) + log(y). Since the two logs above have the same base b, we have: x = 5 and y = 8. So we have: logb(40) = logb(5) + logb(8) logb(40) = 3.56 + 4.61 logb(40) = 8.17