If
2
1+cosA
=x, then the value of x is:
- Asin
2
(
2
A
) - Bsin(
2
A
) - Ccos(
2
A
) - Dcos
2
(
2
A
)
Solution & Step-by-step Explanation
Using the standard trigonometric double-angle/half-angle identity:
cosA=2cos
2
(
2
A
)−1
Rearranging the terms:
1+cosA=2cos
2
(
2
A
)
Dividing both sides by 2:
2
1+cosA
=cos
2
(
2
A
)
Since it is given that
2
1+cosA
=x, we have:
x=cos
2
(
2
A
)
cosA=2cos
2
(
2
A
)−1
Rearranging the terms:
1+cosA=2cos
2
(
2
A
)
Dividing both sides by 2:
2
1+cosA
=cos
2
(
2
A
)
Since it is given that
2
1+cosA
=x, we have:
x=cos
2
(
2
A
)