Prove that: 
(secA + tanA) / (secA - tanA) = 1 + 2 secA tanA  + 2 tan^2 A 

Answer:


Solving these questions are tricky! First you need to eliminate the denominator by changing the denominator into 1.

We know,
sec^2 A - tan^2 A = 1

Now, what do we have to do convert (sec A - tan A ) into sec^2 A - tan^2 A .
Wait I think we need to multiply by
(secA + tan A)

Because we know, (a - b) (a +b) = a^2 - b^2

But to put
(secA + tan A) we need to multiply and divide both by (secA + tan A).

I mean, (sec A + tan A) / (secA + tanA)

And we get the RHS.

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