Question

(sina+cosa)3=3(sina+cosa)-2(sin 3+cos 3)​

Answer 1

`\text{R.H.S}\\\\=3( \sin a + \cos a) - 2( \sin^3 a + \cos^3 a )\\\\=3( \sin a + \cos a) -2 (\sin a + \cos a ) ( \sin^2 a + \cos^2 a - \sin a \cos a) \\\\=3( \sin a + \cos a) - 2 (\sin a + \cos a)(1 - \sin a \cos a)\\\\=(\sin a + \cos a)(3 - 2 +2 \sin a \cos a)\\ \\=( \sin a + \cos a )(1+ 2 \sin a \cos a)\\ \\=( \sin a \cos a )(\sin^2 a + \cos^2 a +2 \sin a \cos a)\\ \\=(\sin a + \cos a)( \sin a + \cos a )^2\\\\= ( \sin a + \cos a )^3 \\\\= \text{L.H.S}\\\\\text{Proved.}`