Question

If sec A-tan A=x, then sec A=

1)(x²+1)/x

2)(x²+1)/2x

3)(x²-1)/2x

4)(x²-1)/x

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Answer 1

Solution :- Given , secA - tanA = x ___(1)

1/x = 1/secA-tanA

Multiply by secA+ tanA in num and denominator .

1/x = secA+tanA/sec²A-tan²A

We know that, sec²x-tan²x = 1

1/x = secA+ tanA_____(2)

Add (1) and (2)

1/x + x = secA- tanA+ secA + tanA

1+x²/x = 2secA

secA= x²+1/2x

•°•Option (2) Is correct

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