1.

If Sec A + Tan A = 4, then the value of (Cot A + 1)/(Cot A – 1) is1. 65/82. – 23/73. 17/194. 11/16

Answer» Correct Answer - Option 2 : – 23/7

Given

Sec A + Tan A = 4

Concept

Sec2 A – Tan2A = 1

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

Calculation

Sec = 4 – Tan A

Squaring on both sides

Sec2A = 16 + Tan2A – 8 Tan A

⇒  1 + Tan2A = 16 + Tan2A – 8 Tan A

⇒  1 – 16 = - 8 Tan A

⇒  15/8 = Tan A

So, Cot A = 8/15

Now, [(8/15) + 1]/[(8/15) – 1]

⇒   [(8 + 15)/15]/[(8 – 15)/15]

⇒   -23/7


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