# If Cosθ +Sin θ= m and Sec θ+ Cosec θ=n then the value of n(m²-1) is equal to:

**Answer: (4) 2 m **

**Explanation:-**

Cosθ +Sin θ= m ………………………… (1)

and Sec θ+ Cosec θ=n

Sec θ+ Cosec θ=n

1/Cosθ + 1/Sinθ = n

(Sinθ + Cosθ)/Cosθ Sinθ = n

n(m² – 1)

Put the value of m = Cosθ +Sin θ & n = (Sinθ + Cosθ)/Cosθ Sinθ

Then, (Sinθ + Cosθ)/Cosθ Sinθ {(Cosθ +Sin θ)² – 1}

= (Sinθ + Cosθ)/Cosθ Sinθ x {Cos²θ + Sin²θ + 2 Cosθ Sinθ – 1}

= (Sinθ + Cosθ)/Cosθ Sinθ x (1 + 2 Cosθ Sinθ – 1}

= (Sinθ + Cosθ)/Cosθ Sinθ x (2 Cosθ Sinθ)

= 2 (Sinθ + Cosθ)

From equation (1),

= 2 m

Hence, the correct answer is option (4) 2 m.