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The value of (sin(pi-alpha))/(sin alpha-...

The value of `(sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha` is

A

`-2`

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`(sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha`
`=(sin alpha)/(sin alpha-cos alpha(sin.(alpha)/(2))/(cos.(alpha)/(2)))-cos alpha`
`=(sin alpha cos.(alpha)/(2))/(sin alpha cos.(alpha)/(2)-cos alpha sin.(alpha)/(2))-cos alpha`
`=(2sin.(alpha)/(2)cos.(alpha)/(2)cos.(alpha)/(2))/(sin(alpha-(alpha)/(2)))-cos alpha`
`=2 "cos"^(2)(alpha)/(2)-cos alpha`
= 1
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