frac{sin 81^circ + cos 81^circ}{sin 81^circ - | vedclass

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Question

(D) Given expression: $E = \frac{\sin 81^\circ + \cos 81^\circ}{\sin 81^\circ - \cos 81^\circ}$Divide the numerator and denominator by $\cos 81^\circ$

Vedclass · Accepted Answer

$	an 54^\circ$

Vedclass · Answer

(D) Given expression: $E = \frac{\sin 81^\circ + \cos 81^\circ}{\sin 81^\circ - \cos 81^\circ}$Divide the numerator and denominator by $\cos 81^\circ$:$E = \frac{	an 81^\circ + 1}{	an 81^\circ - 1}$Since $	an 45^\circ = 1$,we can write:$E = \frac{	an 81^\circ + 	an 45^\circ}{	an 81^\circ - 	an 45^\circ}$Using the formula $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$,this does not directly match. Let us rewrite the expression as:$E = -\frac{1 + 	an 81^\circ}{1 - 	an 81^\circ} = -	an(45^\circ + 81^\circ) = -	an(126^\circ)$Alternatively,using $\sin 81^\circ = \cos 9^\circ$ and $\cos 81^\circ = \sin 9^\circ$:$E = \frac{\cos 9^\circ + \sin 9^\circ}{\cos 9^\circ - \sin 9^\circ} = \frac{1 + 	an 9^\circ}{1 - 	an 9^\circ} = 	an(45^\circ + 9^\circ) = 	an 54^\circ$

$\frac{\sin 81^\circ + \cos 81^\circ}{\sin 81^\circ - \cos 81^\circ}$ is equal to

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