Question

(cosx/1-sinx)-secx=tanx

Answer 1

Answer:

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

Step-by-step explanation:

Given trigonometrical expression as :

( $\dfrac{\textrm cos x}{\textrm 1-sin x}$ ) - sec x = tan x

Or, ( $\dfrac{\textrm cos x}{\textrm 1-sin x}$ ) = tan x + sec x

or,  ( $\dfrac{\textrm cos x}{\textrm 1-sin x}$ ) =  ( $\dfrac{\textrm sin x}{\textrm cos x}$ )  +  ( $\dfrac{\textrm 1}{\textrm cos x}$ )

or,  ( $\dfrac{\textrm cos x}{\textrm 1-sin x}$ ) =  ( $\dfrac{\textrm 1 + sin x}{\textrm cos x}$ )

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