If (1+secA)/tanA=x, then x is
- Acot(A/2)
- Btan(A/2)
- Ccsc(A/2)
- Dsec(A/2)
Solution & Step-by-step Explanation
Given expression:
x=
tanA
1+secA
Convert the terms into sine and cosine:
x=
cosA
sinA
1+
cosA
1
=
cosA
sinA
cosA
cosA+1
=
sinA
1+cosA
Using half-angle trigonometric formulas:
1+cosA=2cos
2
(
2
A
)
sinA=2sin(
2
A
)cos(
2
A
)
Substitute these identities back into the expression:
x=
2sin(
2
A
)cos(
2
A
)
2cos
2
(
2
A
)
=
sin(
2
A
)
cos(
2
A
)
=cot(
2
A
)
x=
tanA
1+secA
Convert the terms into sine and cosine:
x=
cosA
sinA
1+
cosA
1
=
cosA
sinA
cosA
cosA+1
=
sinA
1+cosA
Using half-angle trigonometric formulas:
1+cosA=2cos
2
(
2
A
)
sinA=2sin(
2
A
)cos(
2
A
)
Substitute these identities back into the expression:
x=
2sin(
2
A
)cos(
2
A
)
2cos
2
(
2
A
)
=
sin(
2
A
)
cos(
2
A
)
=cot(
2
A
)