Question

1/secA+tanA = secA - tanA. prove it

Answer 1

1/secA+tanA

Multiply by secA - tanA on both denominator and nominator

(secA - tanA) ÷ (sec²A - tan²A)

We know, sec²A - tan²A = 1

Then,

(secA - tanA) ÷ 1

SecA - tanA


×××××××××××××××××××××××

Hence, proved


I hope this will help you

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Answer 2

Rationalize the left hand side
1/sec A+tanA*secA-tanA /secA,-tanA
secA-tanA/sec2A-tan2A. (sec2A-tan2A=1)
secA-tanA,
Proven