Explain briefly please......Q 9
Explain briefly please......Q 9 EXAMPLE 9 If = sin x cos x and b = cos x sin x, then (a) a—b > 0 fo x e (0, It/4) (b) a —b < 0 for xe (0, Tt/4) (c) a +b < 0 for xe (O, It/ 2) (d) a +b < 0 for xe (0, It/4) Ans. (a) SOLUTION We have, a—b = sinxcosx (cos x —sin x) a—b>0for0 O for O < < O < x < ¯ 2

Dear student

a = {sinxcos}^{3} x b = {cosxsin}^{3} x Consider, a - b = {sinxcos}^{3} x - {cosxsin}^{3} x = sinx cosx (\cos^{2} x - \sin^{2} x) = sinx cosx \cos 2 x [as \cos 2 A = \cos^{2} A - \sin^{2} A] = \frac{2 sinx cosx \cos 2 x}{2} = \frac{\sin 2 x \cos 2 x}{2} [as \sin 2 A = 2 sinAcosA] = \frac{2 \sin 2 x \cos 2 x}{4} = \frac{\sin 4 x}{4} [as \sin 2 A = 2 sinAcosA]

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