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SSC CHSL 8 Jan 2017 Shift 3 Paper

Question : 55 of 100

Marks: +1, -0

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

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=\frac{C+D}{2}

and

y=\frac{C-D}{2}

Substituting above values in equation (iii)

⇒ cosC +cosD = 2cos

\left(\frac{C+D}{2}\right)

cos

\left(\frac{C-D}{2}\right)

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