Question

okay so, how can i verify that cos(x)/(1-sin(x))=sec(x)+tan(x)? I changed the right side to other terms, but then i just came out with cos(x)^2 on the left and zero on the right. any ideas?

Answer 1

square everything and then use the property rules

Answer 2

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



[cos(x)/(1-sin(x))][(1+sin(x))/(1+sin(x))] = sec(x)+tan(x)



[cos(x)(1+sin(x))]/[(1-sin(x))(1+sin(x))] = sec(x)+tan(x)



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



(cos(x)+sin(x)cos(x))/(cos^2(x)) = sec(x)+tan(x)



(cos(x)/(cos^2(x))+(sin(x)cos(x))/(cos^2(x)) = sec(x)+tan(x)



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



sec(x)+tan(x) = sec(x)+tan(x)