△XYZ is right-angled at Y. If m∠Z=45
∘
, then find the value of (cscX−
3
2
).
- A\frac{2-\sqrt{3}}{2\sqrt{3}}
- B\frac{1-\sqrt{6}}{\sqrt{2}}
- C\frac{\sqrt{6}-2}{\sqrt{3}}
- D-\frac{1}{\sqrt{3}}
Solution & Step-by-step Explanation
In △XYZ, it is right-angled at Y, so ∠Y=90
∘
.
Given ∠Z=45
∘
.
Since the sum of angles in a triangle is 180
∘
:
∠X=180
∘
−(90
∘
+45
∘
)=45
∘
Now we need to find the value of cscX−
3
2
:
csc45
∘
=
2
Substitute this value into the expression:
2
−
3
2
=
3
2
⋅
3
−2
=
3
6
−2
∘
.
Given ∠Z=45
∘
.
Since the sum of angles in a triangle is 180
∘
:
∠X=180
∘
−(90
∘
+45
∘
)=45
∘
Now we need to find the value of cscX−
3
2
:
csc45
∘
=
2
Substitute this value into the expression:
2
−
3
2
=
3
2
⋅
3
−2
=
3
6
−2