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1.  If √2 cos A = cos B + cos³B,

√2 sin A = sin B - sin³B.

Then, |sin (A - B)| is equal to

(a) 1/2

(b) 1/3   (Ans)

(c) 2/3

(d) 1/5

Solution :  sin (A - B) = sin A cos B -  cos A sin B        ............(i)

Substituting the values of cos A andsin A from the given Eq. (i),we have

sin (A - B) = - sin B cos B                                        ............(ii)
                          √2

On squaring and adding given equation, we get

cos2B = 1/3

sin (A - B) = ± 1/3