If cos60
∘
−sec30
∘
=x, then the value of x is:
- A1
- B\frac{\sqrt{3}+2}{2}
- C\frac{\sqrt{3}-4}{2\sqrt{3}}
- D\frac{1}{2}
Solution & Step-by-step Explanation
Given expression:
x=cos60
∘
−sec30
∘
We know the standard values of trigonometric ratios:
cos60
∘
=
2
1
sec30
∘
=
cos30
∘
1
=
2
3
1
=
3
2
Substitute these values into the equation:
x=
2
1
−
3
2
Taking the LCM of denominators 2 and
3
, which is 2
3
:
x=
2
3
3
−2×2
x=
2
3
3
−4
x=cos60
∘
−sec30
∘
We know the standard values of trigonometric ratios:
cos60
∘
=
2
1
sec30
∘
=
cos30
∘
1
=
2
3
1
=
3
2
Substitute these values into the equation:
x=
2
1
−
3
2
Taking the LCM of denominators 2 and
3
, which is 2
3
:
x=
2
3
3
−2×2
x=
2
3
3
−4