Proving identity

Question

Prove that (cos x-sin x)/cos x = sin²x-tanx+cos²x

 

Also is there any restrictions?

Answer 1

Hey Star,

 

using the the left hand side

 

( cos x - sin x ) / cos x

 

= 1 - tan x

 

using the right hand side 

 

 

Sin^2 x + cos ^2 x = 1

 

1 - tan x

 

The left hand side is equal to the right hand side thus we have proven the identity.

 

Regards,

 

Mayuran