If A,B,C are angles of a triangle, then `2sinA/2cos e c B/2sinC/2-sinAcotB/2-cosAi s` independent of A,B,C (b) function of A,B function of C (d) none of these

Options

A. independent of `A,B,C`
B. function of A,B
C. function of C
D. none of these.

Answer

A

Explanation

`2sin""(A)/(2)co sec"" (B)/(2)(sin((C)/(2))-cos((A)/(2))cos((B)/(2)))-cosA`.
`2sin((A)/(2))co sec((B)/(2))xx(cos((A+B)/(2))-cos((A)/(2))cos((B)/(2)))-cosA`
`2sin((A)/(2))co sec((B)/(2))(-sin((A)/(2))sin((B)/(2)))-cosA`
`=-2sin^(2)((A)/(2))-cosA=-1`