If cos(
2
A
)=x, then the value of x is:
- A2
1−cosA
- B2
1+sinA
- C2
1−sinA
- D2
1+cosA
Solution & Step-by-step Explanation
From double-angle / half-angle trigonometric identities, we know that:
cos(2θ)=2cos
2
θ−1
Let θ=
2
A
. Substituting this gives:
cosA=2cos
2
(
2
A
)−1
Rearranging the terms to isolate cos(
2
A
):
2cos
2
(
2
A
)=1+cosA
cos
2
(
2
A
)=
2
1+cosA
cos(
2
A
)=
2
1+cosA
Given x=cos(
2
A
), we have:
x=
2
1+cosA
cos(2θ)=2cos
2
θ−1
Let θ=
2
A
. Substituting this gives:
cosA=2cos
2
(
2
A
)−1
Rearranging the terms to isolate cos(
2
A
):
2cos
2
(
2
A
)=1+cosA
cos
2
(
2
A
)=
2
1+cosA
cos(
2
A
)=
2
1+cosA
Given x=cos(
2
A
), we have:
x=
2
1+cosA