Solve the equation tan x sin x if x is in 0 2pi Solutionta

Solve the equation tan x = sin x if x is in ( 0, 2pi ).

tanx = sinx is the given equation to solve for x:

Solution:

Tanx = sinx/cosx, by definition. Substitute this in the given equation.

So the give equation becomes:

sinx/cosx = sinx.

Divide both sides by sinx.

1/cosx = 1.

Cross multiply.

1 = cosx

cosx = 1 when x = 0 or 2npi, n = 0,1,2....

Therefore,

x = 2npi, n =0 , 1 ,2 ,3, ....