Question #1f5ff
2 Answers
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