Question

What is the value of (tan A+ cotA+ secA)( tanA+cotA- secA)​

Answer 1

(tanA+cotA+secA)(tanA+cotA-secA)

=>tanA(tanA+cotA-secA)+cotA(tanA+cotA-secA)+secA(tanA+cotA-secA)

=>tan²A+1-tanAsecA+1+cot²A-cotAsecA+secAtanA+cotAsecA-sec²A {tanAcotA = 1}

=>tan²A+1+cot²A-sec²A+1

=>sec²A+cot²A-sec²A+1 {1+tan²A = sec²A)

=>cot²A+1

=>cosec²A

Cheers!