SOLUTION: ((cos x)/(1-(sin x/cos x)))+((sin x)/(1-(cos x/sin x)))= sin x+ cos x How do you verify this identity?

Algebra ->  Trigonometry-basics -> SOLUTION: ((cos x)/(1-(sin x/cos x)))+((sin x)/(1-(cos x/sin x)))= sin x+ cos x How do you verify this identity?      Log On


   

Question 602535: ((cos x)/(1-(sin x/cos x)))+((sin x)/(1-(cos x/sin x)))= sin x+ cos x
How do you verify this identity?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
cos(x)/(1 - sin(x)/cos(x))+sin(x)/(1 - cos(x)/sin(x)) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+sin(x)/(1 - cot(x)) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+sin(x)/(1 - 1/tan(x)) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+sin(x)/(tan(x)/tan(x) - 1/tan(x)) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+sin(x)/( (tan(x)-1)/tan(x) ) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+sin(x)*( tan(x)/(tan(x)-1) ) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+(sin(x)*tan(x))/( tan(x)-1) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+(sin(x)*tan(x))/( -(-tan(x)+1) ) = sin(x) + cos(x)

cos(x)/(1 - tan(x))+(sin(x)*tan(x))/( -(1 - tan(x)) ) = sin(x) + cos(x)

cos(x)/(1 - tan(x)) - (sin(x)*tan(x))/(1 - tan(x)) = sin(x) + cos(x)

(cos(x) - sin(x)*tan(x))/(1 - tan(x)) = sin(x) + cos(x)

(cos(x) - sin(x)*(sin(x)/cos(x)))/(1 - tan(x)) = sin(x) + cos(x)

(cos(x) - sin^2(x)/cos(x))/(1 - tan(x)) = sin(x) + cos(x)

(cos^2(x)/cos(x) - sin^2(x)/cos(x))/(1 - tan(x)) = sin(x) + cos(x)

((cos^2(x) - sin^2(x))/cos(x))/(1 - tan(x)) = sin(x) + cos(x)

((cos^2(x) - sin^2(x))/cos(x))*(1/(1 - tan(x))) = sin(x) + cos(x)

(cos^2(x) - sin^2(x))/(cos(x)(1 - tan(x))) = sin(x) + cos(x)

(cos^2(x) - sin^2(x))/(cos(x) - cos*tan(x)) = sin(x) + cos(x)

(cos^2(x) - sin^2(x))/(cos(x) - cos(x)*sin(x)/cos(x)) = sin(x) + cos(x)

(cos^2(x) - sin^2(x))/(cos(x) - sin(x)) = sin(x) + cos(x)

((cos(x) - sin(x))(cos(x) + sin(x)))/(cos(x) - sin(x)) = sin(x) + cos(x)

cos(x) + sin(x) = sin(x) + cos(x)

sin(x) + cos(x) = sin(x) + cos(x)

This verifies the identity.