If F=2/(sinθ+cosθ) then the minimum value of F out of the following option is (NEET)

If F=2/(sinθ+cosθ) then the minimum value of F out of the following option is

1. 1

2. 1/√2

3. 3/√2

4. √2

If F=2/(sinθ+cosθ) then the minimum value of F out of the following option is

Solution

We have,

Multiply and divide by √2 in denominator

We Get,

Now,

Using Identity, sinAcosB+cosAsinB=sin(A+B)

Now,

Maximum value of sine function is 1.

So, we have,

Therefore,

Hence, option (4) is correct answer.