Hi, I am a little confused on how to isolate y from (y)/(k-y) = tanx=(sin^2x)/(cos^2x)? The answer should be y=ksin²x Any help is much appreciated! Thank you in advance

Question

Hi, I am a little confused on how to isolate y from
`(y)/(k-y) = tanx=(sin^2x)/(cos^2x)`?

The answer should be y=ksin²x

Any help is much appreciated! Thank you in advance

Answer 1

Explanation:

Not sure what ' tan x' is doing in there, because it is not true

Anyway:

Multiply both sides of the equation by k- y to get

y = (k-y) sin2 / cos2 now multiply both sides by cos^2

y cos^2 = (k-y) sin^2 expand R side

y cos^2 = ( k sin^2 - y sin^2 ) add y sin^2 to both sides

y cos^2 + y sin^2 = k sin^2 factor out 'y'

y ( cos^2 + sin^2) = k sin^2 remember : sin^2 + cos^2 =1

y ( 1) = k sin^2

y = k sin^2