Consider angles `alpha = (2n+(1)/(2))pi pm A` and `beta = m pi +(-1)^(m)((pi)/(2)-A)` where n, m `in` I. Which of the following is not true ?

Options

A. `alpha` and `beta` are always the same angles
B. `alpha` and `beta` are co-terminal angles
C. `sin alpha = sin beta` but `cos alpha ne cos beta`
D. none of these

Answer

C

Explanation

Let m = 2k, i.e. m is even where `k in I`
`therefore beta = 2k pi + (pi)/(2)-A=(2k+(1)/(2))pi -A` ….(1)
If m = 2k + 1, i.e., m is odd, then
`therefore beta = (2k+1)pi-((pi)/(2)-A)=(2k+(1)/(2))pi+A` …..(2)
From (1) and (2), `beta` can be expressed as
`beta = (2k+(1)/(2))pi pm A, k in I`
which is same as `alpha`.