Question

The value of `(sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha` is
A. `-2`
B. `-1`
C. 1
D. 2

Answer 1

Correct Answer - 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