Evaluate:sin 25^{circ} cos 65^{circ} + cos 25 | vedclass

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Question

(D) The given expression is $\sin 25^{\circ} \cos 65^{\circ} + \cos 25^{\circ} \sin 65^{\circ}$.We know that $\cos(90^{\circ} - 	heta) = \sin 	heta$

Vedclass · Accepted Answer

$1$

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(D) The given expression is $\sin 25^{\circ} \cos 65^{\circ} + \cos 25^{\circ} \sin 65^{\circ}$.We know that $\cos(90^{\circ} - 	heta) = \sin 	heta$ and $\sin(90^{\circ} - 	heta) = \cos 	heta$.Substituting $\cos 65^{\circ} = \cos(90^{\circ} - 25^{\circ}) = \sin 25^{\circ}$ and $\sin 65^{\circ} = \sin(90^{\circ} - 25^{\circ}) = \cos 25^{\circ}$:$= (\sin 25^{\circ})(\sin 25^{\circ}) + (\cos 25^{\circ})(\cos 25^{\circ})$$= \sin^{2} 25^{\circ} + \cos^{2} 25^{\circ}$Using the identity $\sin^{2} A + \cos^{2} A = 1$,we get:$= 1$

Evaluate:
$\sin 25^{\circ} \cos 65^{\circ} + \cos 25^{\circ} \sin 65^{\circ}$

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Evaluate:$\sin 25^{\circ} \cos 65^{\circ} + \cos 25^{\circ} \sin 65^{\circ}$