How do you verify the identity #sqrt((1+sintheta)/(1-sintheta))=(1+sintheta)/abscostheta#?

Question

7209 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-17T18:48:05

see below

Left Hand Side:

#sqrt ((1+sin theta)/(1-sin theta))=sqrt ((1+sin theta)/(1-sin theta) *((1+sin theta)/(1+sin theta))#

#=sqrt ((1+sin theta)^2/(1-sin ^2theta))#

#=sqrt ((1+sin theta)^2/(cos ^2theta))#

#=sqrt ((1+sin theta)^2) / sqrt (cos^2 theta)#

#=(1+sin theta)/abs( cos theta)# since #sqrt(x^2) = abs(x)#

#:.=# Right Hand Side