Question

(cosx/1-sinx)-secx=tanx

Answer 1

The value of given trigonometrical expression is cos²x + sin²x = 1

Explanation:

Given trigonometrical expression as :

(
`(\textrm cos x)/(\textrm 1-sin x)` ) - sec x = tan x

Or, (
`(\textrm cos x)/(\textrm 1-sin x)` ) = tan x + sec x

or, (
`(\textrm cos x)/(\textrm 1-sin x)` ) = (
`(\textrm sin x)/(\textrm cos x)` ) + (
`(\textrm 1)/(\textrm cos x)` )

or, (
`(\textrm cos x)/(\textrm 1-sin x)` ) = (
`(\textrm 1 + sin x)/(\textrm cos x)` )

Now, cross multiplying both side

I.e (cos x) × (cos x) = ( 1 - sin x ) × ( 1 + sin x )

or, cos²x = 1 - sin² x

or, cos²x + sin²x = 1

So, Value of expression is cos²x + sin²x = 1

Hence The value of given trigonometrical expression is cos²x + sin²x = 1 answer