sin {163^circ} cos {347^circ} + sin {73^circ} | vedclass

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Question

(B) Given expression: $\sin {163^\circ} \cos {347^\circ} + \sin {73^\circ} \sin {167^\circ}$ Using the reduction formulas: $\sin {163^\circ} = \sin (1

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(B) Given expression: $\sin {163^\circ} \cos {347^\circ} + \sin {73^\circ} \sin {167^\circ}$ Using the reduction formulas: $\sin {163^\circ} = \sin (180^\circ - 17^\circ) = \sin {17^\circ}$ $\cos {347^\circ} = \cos (360^\circ - 13^\circ) = \cos {13^\circ}$ $\sin {73^\circ} = \sin (90^\circ - 17^\circ) = \cos {17^\circ}$ $\sin {167^\circ} = \sin (180^\circ - 13^\circ) = \sin {13^\circ}$ Substituting these values into the expression: $= \sin {17^\circ} \cos {13^\circ} + \cos {17^\circ} \sin {13^\circ}$ Using the identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$: $= \sin (17^\circ + 13^\circ) = \sin {30^\circ}$ Since $\sin {30^\circ} = 1/2$,the final answer is $1/2$.

$\sin {163^\circ} \cos {347^\circ} + \sin {73^\circ} \sin {167^\circ} = $

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