If x = a sin theta - b cos theta and y = a co | vedclass

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(B) Given equations are:$x = a \sin 	heta - b \cos 	heta$ ..... $(1)$$y = a \cos 	heta + b \sin 	heta$ ..... $(2)$Squaring both equations:$x^{2} =

Vedclass · Accepted Answer

$x^{2} + y^{2} = a^{2} + b^{2}$

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(B) Given equations are:$x = a \sin 	heta - b \cos 	heta$ ..... $(1)$$y = a \cos 	heta + b \sin 	heta$ ..... $(2)$Squaring both equations:$x^{2} = (a \sin 	heta - b \cos 	heta)^{2} = a^{2} \sin^{2} 	heta + b^{2} \cos^{2} 	heta - 2ab \sin 	heta \cos 	heta$ ..... $(3)$$y^{2} = (a \cos 	heta + b \sin 	heta)^{2} = a^{2} \cos^{2} 	heta + b^{2} \sin^{2} 	heta + 2ab \sin 	heta \cos 	heta$ ..... $(4)$Adding equations $(3)$ and $(4)$:$x^{2} + y^{2} = a^{2} \sin^{2} 	heta + b^{2} \cos^{2} 	heta - 2ab \sin 	heta \cos 	heta + a^{2} \cos^{2} 	heta + b^{2} \sin^{2} 	heta + 2ab \sin 	heta \cos 	heta$$x^{2} + y^{2} = a^{2} (\sin^{2} 	heta + \cos^{2} 	heta) + b^{2} (\cos^{2} 	heta + \sin^{2} 	heta)$Since $\sin^{2} 	heta + \cos^{2} 	heta = 1$,we get:$x^{2} + y^{2} = a^{2}(1) + b^{2}(1)$$x^{2} + y^{2} = a^{2} + b^{2}$

If $x = a \sin \theta - b \cos \theta$ and $y = a \cos \theta + b \sin \theta$,then which of the following is true?

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