Question

CosA-sinA +1 /CosA+sinA-1 = SinA/1-cosA

Answer 1

Answer:

Step-by-step explanation:

(cosA-sinA)+1/(cosA+sinA)-1

doing the rationalization of the denominator (cosA+sinA)-1

(cosA-sinA)+1/(cosA+sinA)-1  × [(cosA+sinA)+1/(cosA+sinA)+1]

on multiplying we get -:

=[cos2A-sin2A+2cosA+1]/2sinAcosA

=[cos2A-sin2A+2cosA+sin2A+cos2A]/2sinAcosA                  

=[2cos2A+2cosA]/2sinAcosA

=[cosA+cos2A]/sinAcosA

This can also be written as-:

=cosA/sinAcosA  +cos2A/sinAcosA

CosecA+cotA =R.H.S