Question

If cosx=sinx then find value of tan²x-tanx

Answer 1

Hi friend,


Given,

Cos x= sin x

Then ,tan x= sin x/cos x

Sin²x/cos²x= tan²x

Since ,sin x= cos x

Sin²x/cos²x -sinx/cos x

On cancelling,

Tan²x-tan x= 1-1

Tan²x-tan x= 0.

Hope this helped you a little!!!

Answer 2

Given,
cosx = sinx

Transposing the terms we get

cosx/sinx= 1 or sinx/cosx=1 .

We know that;

tanx = sinx/ cosx = 1

tanx = 1 .

Now, tan²x - tanx

= tanx ( tanx - 1 )

= 1 ( 1 - 1 )

= 1 * 0

= 0 .

(or)

tan²x-tanx

= 1 ² - 1

= 1 - 1

= 0

Therefore, For the given condition; tan²x-tanx = 0