Question

tanx+secx =e^x, then cosx=?

Answer 1

Given: tanx + secx = e^x

To find: Value of cosx?

Solution:

• Now we have given tanx + secx = e^x.

• We can write it as:

              1 + sinx / cosx = e^x

• Now we know that 1 + sinx = cos x/2 + sin x/2 and cos x = cos x/2 - sin x/2.

             cos x/2 + sin x/2 / cos x/2 - sin x/2 = e^x

• Now using componendo and dividendo, we get:

             tan x/2 = e^x - 1 / e^x + 1

• Now cos x = 1 - tan² x/2 / 1 + tan² x/2

• Putting value of tan x, we get:

             cos x = 1 - (e^x - 1 / e^x + 1)²  / 1 + (e^x - 1 / e^x + 1)²

• After solving, we get:

             cos x = 2e^x / (e^2x + 1)

             cos x = 2 / (e^x + e^-x)

Answer:

         So the value of cos x is 2 / (e^x + e^-x)