1.

If x = Sec A/(1 – Cos A), then Sin2A/(Sec A + 1) is equal to?1. (1 – Cos A)/ Sec A2. cot A/(1 – Sec A)3. Tan A/(1 + Cot A)4. Sec A/(1 + Cos A)

Answer» Correct Answer - Option 1 : (1 – Cos A)/ Sec A

Identity used:

Sin2A = 1 – Cos2A 

Calculation:

x = {[Sec A/(1 – Cos A)] × (1 + CosA)/(1 + CosA)

⇒  x = (Sec A + Sec A Cos A)/(1 – CosA) × (1 + CosA)

⇒ x = (SecA + 1)/(1 – Cos2A)

⇒  x = (Sec A + 1)/Sin2A

⇒  1/x = Sin2A/(Sec A + 1)

So, value of Sin A/(Sec A + 1) is (1 – Cos A)/Sec A


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