If tan(
2
A
)=x, then the value of x is:
- A1−cosA
sinA
- B1+cosA
sinA
- CsinA
1+cosA
- DsinA
1−cosA
Solution & Step-by-step Explanation
We know the standard half-angle trigonometric identities:
sinA=2sin(
2
A
)cos(
2
A
)
1+cosA=2cos
2
(
2
A
)
Let us evaluate option B:
1+cosA
sinA
=
2cos
2
(
2
A
)
2sin(
2
A
)cos(
2
A
)
Canceling out 2cos(
2
A
) from the numerator and denominator:
1+cosA
sinA
=
cos(
2
A
)
sin(
2
A
)
=tan(
2
A
)=x
Hence, x=
1+cosA
sinA
.
sinA=2sin(
2
A
)cos(
2
A
)
1+cosA=2cos
2
(
2
A
)
Let us evaluate option B:
1+cosA
sinA
=
2cos
2
(
2
A
)
2sin(
2
A
)cos(
2
A
)
Canceling out 2cos(
2
A
) from the numerator and denominator:
1+cosA
sinA
=
cos(
2
A
)
sin(
2
A
)
=tan(
2
A
)=x
Hence, x=
1+cosA
sinA
.