sin^{2} 15^{circ} + sin^{2} 75^{circ} = dots | vedclass

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Question

(A) We know that $\sin(90^{\circ} - 	heta) = \cos 	heta$.Therefore,$\sin 75^{\circ} = \sin(90^{\circ} - 15^{\circ}) = \cos 15^{\circ}$.Substituting

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) We know that $\sin(90^{\circ} - 	heta) = \cos 	heta$.Therefore,$\sin 75^{\circ} = \sin(90^{\circ} - 15^{\circ}) = \cos 15^{\circ}$.Substituting this into the expression:$\sin^{2} 15^{\circ} + \sin^{2} 75^{\circ} = \sin^{2} 15^{\circ} + (\cos 15^{\circ})^{2}$$= \sin^{2} 15^{\circ} + \cos^{2} 15^{\circ}$.Using the trigonometric identity $\sin^{2} 	heta + \cos^{2} 	heta = 1$,we get:$= 1$.

$\sin^{2} 15^{\circ} + \sin^{2} 75^{\circ} = \dots$

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