frac{cos 9^circ + sin 9^circ}{cos 9^circ - si | vedclass

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Question

(A) Divide the numerator and the denominator by $\cos 9^\circ$:$\frac{\frac{\cos 9^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 9^\circ}}{\frac{\co

Vedclass · Accepted Answer

$	an 54^\circ$

Vedclass · Answer

(A) Divide the numerator and the denominator by $\cos 9^\circ$:$\frac{\frac{\cos 9^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 9^\circ}}{\frac{\cos 9^\circ}{\cos 9^\circ} - \frac{\sin 9^\circ}{\cos 9^\circ}} = \frac{1 + 	an 9^\circ}{1 - 	an 9^\circ}$Since $	an 45^\circ = 1$,we can write this as:$\frac{	an 45^\circ + 	an 9^\circ}{1 - 	an 45^\circ 	an 9^\circ}$Using the trigonometric identity $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$,where $A = 45^\circ$ and $B = 9^\circ$:$	an(45^\circ + 9^\circ) = 	an 54^\circ$.

$\frac{\cos 9^\circ + \sin 9^\circ}{\cos 9^\circ - \sin 9^\circ} = $

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