If sin(A/2)=x, then the value of x is
- A2
1+cosA
- B2
1−cosA
- C2
1−sinA
- D2
1+sinA
Solution & Step-by-step Explanation
Using the standard trigonometric double-angle formula for cosine:
cosA=1−2sin
2
(
2
A
)
Rearrange the terms to solve for sin
2
(
2
A
):
2sin
2
(
2
A
)=1−cosA
sin
2
(
2
A
)=
2
1−cosA
Taking the square root on both sides:
sin(
2
A
)=
2
1−cosA
Since sin(A/2)=x, we have x=
2
1−cosA
.
cosA=1−2sin
2
(
2
A
)
Rearrange the terms to solve for sin
2
(
2
A
):
2sin
2
(
2
A
)=1−cosA
sin
2
(
2
A
)=
2
1−cosA
Taking the square root on both sides:
sin(
2
A
)=
2
1−cosA
Since sin(A/2)=x, we have x=
2
1−cosA
.