If cosx + $$\frac{1}{cosx}$$ = 2 , then find the value of $$cos^nx + \frac{1}{cos^nx}$$​​

Correct option is D

Given:

​$$cosx + \frac{1}{cosx} = 2$$ 

Solution:

Let cos x = a Then the equation becomes: 

​$$a+\frac{1}{a}= 2$$ 

​Multiply through by a (assuming $$a\neq0$$ )

$$a^2+1 =2a$$ 

$$a^2-2a+1 = 0$$ 

​Factorize: 

​$$(a-1)^2=0$$ 

a = 1 

cos x = 1

Generalize for $$cos^nx+\frac{1}{cos^nx}$$ 

Since cos x = 1 

​$$cos^nx=1^n =1$$ 

Substitute into the expression: 

​$$cos^nx+\frac{1}{cos^nx}$$ = $$1+\frac{1}{1}$$ =1+1 = 2

$$cos^nx+\frac{1}{cos^nx}$$ = 2

Thus, correct answer is (d) 2