Question #1f5ff

2 Answers
Mar 12, 2017

Let us start with the LHS:

#LHS = ((sintheta+costheta)/sintheta)-((costheta-sintheta)/costheta)#

#" " = ((sintheta+costheta)costheta-(costheta-sintheta)sintheta)/(sinthetacostheta)#

#" " = ((sinthetacostheta+cos^2theta)-(costhetasintheta-sin^2theta))/(sinthetacostheta)#

#" " = (sinthetacostheta+cos^2theta-costhetasintheta+sin^2theta)/(sinthetacostheta)#

#" " = (cos^2theta+sin^2theta)/(sinthetacostheta)#

#" " = (1)/(sinthetacostheta)#

#" " = 1/sintheta*1/costheta#

#" " = csctheta*sectheta#

#" " = RHS \ \ \ \ # QED

Mar 13, 2017

#LHS=(sintheta+costheta)/sintheta-(costheta-sintheta)/costheta#

#=sintheta/sintheta+costheta/sintheta-costheta/costheta+sintheta/costheta#

#=cancel1+costheta/sintheta-cancel1+sintheta/costheta#

#=(cos^2theta+sin^2theta)/(sinthetacostheta)#

#=1/(sinthetacostheta)#

#=secthetacsctheta=RHS#