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If Sec A + Tan A = a, then what is the value of 2Sin A.Sec A/(Sec A - Tan A)?


1. a- 1
2. a- a
3. a(a- 1)
4. a + a2

1 Answer

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Best answer
Correct Answer - Option 1 : a- 1

Given:

SecA + TanA = a

Formula Used:

Sec2A - Tan2A = 1

SinA.SecA = TanA

(a + b)2 = a2 + 2ab + b2

a2 – b2 = (a + b) (a - b)

Calculation:

Sec2A - Tan2A = 1

⇒ (SecA - TanA) × (SecA + TanA) = 1

⇒ (SecA - TanA) × a = 1

⇒ SecA - TanA = 1/a        ----(1)

⇒ SecA + TanA = a        ----(2)

On subtracting equation (1) from (2), we get

2TanA = a - 1/a

⇒ TanA = 1/2(a - 1/a)

As we know that,

SinA.SecA = TanA

So, 2SinA.SecA/(SecA - TanA) = 2TanA/(SecA - TanA)

⇒ 2TanA/(SecA - TanA) = 2 × {1/2(a - 1/a)}/1/a

⇒ 2TanA/(SecA - TanA) = a- 1

The value of 2SinA.SecA/(SecA - TanA) = a- 1.

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