SSC CHSL 8 Jan 2017 Shift 3 Paper

Question : 55 of 100

Marks: +1, -0

If cosC + cosD = x, then value of x is

2cos[(C+D)/2]cos[(C-D)/2]
2sin[(C+D)/2]sin[(C-D)/2]
2cos[(C+D)/2]sin[(C-D)/2]
2sin[(C+D)/2]cos[(C-D)/2]

Solution:

We know that, cos (x+y) = cosx cosy-sinx siny ------(i)
and cos(x-y) = cosx cosy+sinx siny ----(ii)
Adding equations (i) and (ii), we get :
cos(x+y) +cos(x-y) = 2 cosx cosy -------(iii)
Let x + y =C and x-y = D
⇒

x={C+D}/2

and

y={C-D}/2

Substituting above values in equation (iii)
⇒ cosC +cosD = 2cos

({C+D}/2)

cos

({C-D}/2)

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