Select the most appropriate option to solve the equation:

Cos A/(1 - Sin A) = ?

This question was previously asked in

UPSSSC Mandi Inspector Official Paper 1 (Held On : 30 May 2019 Shift 1)

Option 1 : sec A + tan A

**Given:**

The equation = Cos A/(1 - Sin A)

**Formula Used:**

Sin^{2}θ + Cos^{2}θ = 1

**Calculation:**

According to the question, we have

Cos A/(1 - Sin A) ....(1)

Now, multiply in the numerator and denominator of the equation (1) by (1 + Sin A)

= {Cos A × (1 + Sin A)}/{(1 - Sin A)(1 + Sin A)}

⇒ {Cos A × (1 + Sin A)}/(1 - Sin^{2} A)

⇒ {Cos A × (1 + Sin A)}/Cos^{2} A

⇒ (1 + Sin A)/Cos A

⇒ Sec A + Tan A

**∴ The answer of the given equation is Sec A + Tan A.**