If sec A- tan A = √2 tanA, then show that secA + tan A = √2 secA.
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Answer:
LHS=
secA+tanA
secA−tanA
=
secA+tanA
secA−tanA
×
secA−tanA
secA−tanA
=
sec
2
A−tan
2
A
sec
2
A−2secAtanA+tan
2
A
=1+tan
2
A−2secAtanA+tan
2
A
=1−2secAtanA+2tan
2
A
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