Question

Find the value of cos²⁵θ + sec⁵⁰θ, if cosθ + secθ = 2. 
1. 1
2. 25
3. 50
4. 2

Answer 1

Correct Answer - Option 4 : 2

Given :

cosθ + secθ = 2 

Calculations :

Cosθ + secθ = 2 

Cosθ + (1/cosθ) = 2 

(cos²θ + 1)/cosθ = 2 

cos2θ - 2 cosθ + 1 = 0 

cos2θ - cosθ - cosθ + 1 = 0 

cosθ - 1 = 0 

cosθ = 1 and secθ = 1 

So,

 cos25θ + sec50θ = (1)²⁵ + (1)⁵⁰

⇒ 1 + 1 

⇒ 2 

∴  cos25θ + sec50θ is equal to 2 when cosθ + secθ is equal to 2