If cos45
∘
−sec60
∘
=x, then the value of x is:

We are given the equation:
x=cos45
∘
−sec60
∘

We know the standard values of trigonometric ratios:

cos45
∘
=
2

​

1
​

sec60
∘
=
cos60
∘

1
​
=
1/2
1
​
=2
Substituting these values into the equation:

x=
2

​

1
​
−2
Taking the common denominator:

x=
2

​

1−2
2

​

​

This matches option C.