If secA-tanA = root2 tanA then show that secA+ tanA = root2 secA

PFA

Given: secA - tanA = √2 tanATo prove: secA+tanA=√2secAProof: SecA-tanA= √2tanA =>secA-tanA -√2tanA =0 => -secA+tanA+√2tanA=0 => tanA+√2tanA= secA tanA(1+√2)=secA tanA =secA/1+√2On rationalizing we gettanA= secA-√2secA/-1 Substituting this value of tanAWe getSecA+tanA=secA+ secA-√2secA /-1On taking LCM = -secA+secA -√2secA/-1-secA and+secA get cancelled=-√2secA/-1Negative sign will get cancelled=√2secAHence proved