Question

If CosA + SecA = 2 then what will be the value of Cos¹⁶A + Sec¹⁶A?

Answer 1

Correct Answer - Option 3 : 2

Given:

CosA + SecA = 2 

Formula used:

Secθ = 1/Cosθ

Calculation:

Let CosA be x

⇒ SecA = 1/x

We have given,

CosA + SecA = 2 

⇒ x + 1/x = 2

⇒ x = 1

Now, we have to find the value of 

cos¹⁶A + sec¹⁶A

⇒ (x)¹⁶ + (1/x)¹⁶

⇒ (1)¹⁶ + (1/1)¹⁶

⇒ 1 + 1

⇒ 2

∴ The value of cos¹⁶A + sec¹⁶A is 2