frac{{cos {{10}^o} + sin {{10}^o}}}{{cos {{10 | vedclass

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Question

(A) To solve the expression $\frac{{\cos {{10}^o} + \sin {{10}^o}}}{{\cos {{10}^o} - \sin {{10}^o}}}$,divide both the numerator and the denominator by

Vedclass · Accepted Answer

$	an {55^o}$

Vedclass · Answer

(A) To solve the expression $\frac{{\cos {{10}^o} + \sin {{10}^o}}}{{\cos {{10}^o} - \sin {{10}^o}}}$,divide both the numerator and the denominator by $\cos {{10}^o}$:$= \frac{{\frac{{\cos {{10}^o}}}{{\cos {{10}^o}}} + \frac{{\sin {{10}^o}}}{{\cos {{10}^o}}}}}{{\frac{{\cos {{10}^o}}}{{\cos {{10}^o}}} - \frac{{\sin {{10}^o}}}{{\cos {{10}^o}}}}}$$= \frac{{1 + 	an {{10}^o}}}{{1 - 	an {{10}^o}}}$Since $	an {45^o} = 1$,we can write this as:$= \frac{{	an {{45}^o} + 	an {{10}^o}}}{{1 - 	an {{45}^o} \cdot 	an {{10}^o}}}$Using the trigonometric identity $	an(A + B) = \frac{{	an A + 	an B}}{{1 - 	an A \cdot 	an B}}$,where $A = {45^o}$ and $B = {10^o}$:$= 	an({45^o} + {10^o}) = 	an {55^o}$.

$\frac{{\cos {{10}^o} + \sin {{10}^o}}}{{\cos {{10}^o} - \sin {{10}^o}}} = $

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