Cos x tan x - cos x =0

cosx*sinx/cosx-cosx=0   //sinx=cosx///π/4/π+π/4

Step-by-step explanation:

x = π/2 + πn or x = π/4 + πn

Step-by-step explanation:

We are given:

(cosx) * (tanx) - (cosx) = 0

Notice that both terms on the left contain cosx, so we can factor that out. When we do so, we get:

cosx * (tanx - 1) = 0

Now, use the Zero Product Property. Since cosx times (tanx - 1) equals 0, then either cosx = 0, tanx - 1 = 0, or both. So, let's set them equal to 0:

cosx = 0

When is cosx = 0? Think about the unit circle; it's when x = π/2 + πn, where n is any whole number (positive or negative). For example, x = π/2 and x = 3π/2 works.

Now, look at tanx - 1 = 0. Adding 1 to both sides:

tanx = 1

When is tanx = 1? Again, think back to the unit circle; it's when x = π/4 + πn where n is again any whole number (positive or negative).

Since the problem didn't give any bounds, then we can say that:

x = π/2 + πn or x = π/4 + πn

If, however, the problem said that 0 ≤ x ≤ π/2, then we'd simply have x = π/4 or x = π/2.

~ an aesthetics lover