# In the following

(a) sin (x + y) sin(x – y)

= (sin x.cos y + sin y.cos x)( sin x.cos y - sin y.cos x)

= sin2x cos2y+ sin y.cos x. sin x.cos y- sin x.cos y sin y.cos x- sin2y cos2x

= sin2x cos2y- sin2y cos2x

= sin2x(1- sin2y)- sin2y(1- sin2x)

= sin2x- sin2x sin2y- sin2y+ sin2x sin2y

= sin2x – sin2y

(a) matches with (iv)

(b) cos(x + y) cos(x – y)

= (cos x.cos y−sin x.sin y)( cos x.cosy+sin x.siny)

= (cos2x cos2y+ cos x.cos y sin x.siny- sin x.sin y cos x.cosy- sin2x sin2y)

= cos2x cos2y- sin2x sin2y

= cos2x(1- sin2y)-(1- cos2x) sin2y

= cos2x- cos2x sin2y- sin2y+ cos2x sin2y

= cos2x – sin2y

(b) matches with (i)

(c)

(c) matches with (ii)

(c)

(d) matches with (iii)

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