Respuesta :
Answer:
The value of given trigonometrical expression is cos²x + sin²x = 1
Step-by-step explanation:
Given trigonometrical expression as :
( [tex]\dfrac{\textrm cos x}{\textrm 1-sin x}[/tex] ) - sec x = tan x
Or, ( [tex]\dfrac{\textrm cos x}{\textrm 1-sin x}[/tex] ) = tan x + sec x
or, ( [tex]\dfrac{\textrm cos x}{\textrm 1-sin x}[/tex] ) = ( [tex]\dfrac{\textrm sin x}{\textrm cos x}[/tex] ) + ( [tex]\dfrac{\textrm 1}{\textrm cos x}[/tex] )
or, ( [tex]\dfrac{\textrm cos x}{\textrm 1-sin x}[/tex] ) = ( [tex]\dfrac{\textrm 1 + sin x}{\textrm cos x}[/tex] )
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
