I'm only going to alter the left hand side. The right side will stay the same the entire time
I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
So with that in mind, this is how the steps would look:
tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x
Identity is confirmed
This is the worksheet I’m doing https://www.manhassetschools.org/cms/lib8/NY01913789/Centricity/Domain/710/Aim%2082%20Pd%209%20KEY.pdf
Ummm search it up on google it should be on there
I’m not completely sure, but I would say about 3/5 because of the fact that the X is not directly in the middle, so it can’t be 1/2 but it’s very close to the middle which could make it possible that it is 3/5?
