Prove that: 
1 / (secA -tanA) - 1/ cosA = 1/ cosA - 1/(secA + tanA)

Answer:


This question is about tricky!
We need to rationalize the first term of LHS initially.
Then change 1/ cosA into secA

Once you rationalize the first term, you will get secA +tanA and -secA which means you will get secA +tanA -secA in the LHS.

Now, don't do a mistake by cancelling the +secA and -secA.

Now, take secA alone which will be equal to your 1/ cosA in the RHS.
Now you need to get - 1/ (secA +tanA)

For this you need to rationalize (tanA - secA) by taking - sign common.

Identity used:

Sec²x - tan²x = 1

This is how you prove the given trigonometric identity,
1 / (secA -tanA) - 1/ cosA = 1/ cosA - 1/(secA + tanA)
Of Trigonometry in mathematics.

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