frac{{sin 3theta - cos 3theta }}{{sin theta + | vedclass

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Question

(a) Let $\frac{{\sin 3	heta - \cos 3	heta }}{{\sin 	heta + \cos 	heta }} = \frac{N}{D}$(say)

Then $N = 3\sin 	heta - 4{\sin ^3}	heta - (4{\co

Vedclass · Accepted Answer

$2\sin 2	heta $

Vedclass · Answer

(a) Let $\frac{{\sin 3	heta - \cos 3	heta }}{{\sin 	heta + \cos 	heta }} = \frac{N}{D}$(say)

Then $N = 3\sin 	heta - 4{\sin ^3}	heta - (4{\cos ^3}	heta - 3\cos 	heta )$

$ = 3(\sin 	heta + \cos 	heta ) - 4({\sin ^3}	heta + {\cos ^3}	heta )$

$ = (\sin 	heta + \cos 	heta )\{ 3 - 4({\sin ^2}	heta - \sin 	heta \cos 	heta + {\cos ^2}	heta )\} $

$	herefore \;\frac{N}{D} + 1 $

$=  \frac{{(\sin 	heta + \cos 	heta )\{ 3 - 4(1 - \sin 	heta \cos 	heta )\} }}{{\sin 	heta + \cos 	heta }} + 1$

$ = 3 - 4(1 - \sin 	heta \cos 	heta ) + 1$

$ = 4\sin 	heta \cos 	heta = 2\sin 2	heta $.

$\frac{{\sin 3\theta - \cos 3\theta }}{{\sin \theta + \cos \theta }} + 1 = $

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