Question

If m = cosA - sinA and n = cosA + sinA, then show that√m/n+√n/m = 2/√1 - tan^2 A

Answer 1

=Given, m=cosA

=−sinAn=cosA+sinASo mn−nm=m2−

=n2mn=(cosA−sinA)2−(cosA+sinA)2cos2A

=−sin2A=cos2A+sin2A−2sinAcosA−cos2A=−sin2A

==−2sinAcosAcos2A−sin2A=−4sinAcosAcos2A

=−sin2A=−4sinAcosAsinAcosAcos2AsinAcosA−

=sin2AsinAcosA=−4cotA−tanA

hope it helps