How do you verify the identify (sintheta+costheta)/sintheta=1+cottheta?

2 Answers
Aug 2, 2016

Recall that tantheta = (sintheta)/costheta and cottheta = 1/tantheta

Explanation:

(sintheta + costheta)/(sintheta) = (sintheta)/(sintheta) + (costheta)/(sintheta) = 1 + 1/(tantheta) = 1 + cottheta

Aug 2, 2016

see explanation.

Explanation:

There are 3 possible approaches that may be taken.

(1) Manipulate the left side to obtain the right side.

(2) Manipulate the right side to obtain the left side.

(3) Manipulate both sides until they are the same.

Using (1) along with the following color(blue)" trig. identity"

color(orange)" Reminder"

color(red)(|bar(ul(color(white)(a/a)color(black)(cottheta=(costheta)/(sintheta))color(white)(a/a)|)))

left side =(sintheta+costheta)/sintheta

divide terms on numerator by sintheta

rArrcancel(sintheta)/cancel(sintheta)+(costheta)/(sintheta)

rArr (sintheta+costheta)/sintheta=1+cottheta=" right side"rArr" verified"