(1 - tan 348^{circ})(1 + cot 417^{circ}) is e | vedclass

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(B) First,simplify the angles using periodicity: $	an 348^{\circ} = 	an(360^{\circ} - 12^{\circ}) = -	an 12^{\circ}$ $\cot 417^{\circ} = \cot(360^{

Vedclass · Accepted Answer

$2$

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(B) First,simplify the angles using periodicity: $	an 348^{\circ} = 	an(360^{\circ} - 12^{\circ}) = -	an 12^{\circ}$ $\cot 417^{\circ} = \cot(360^{\circ} + 57^{\circ}) = \cot 57^{\circ} = 	an(90^{\circ} - 57^{\circ}) = 	an 33^{\circ}$ Now,the expression is $(1 - (-	an 12^{\circ}))(1 + 	an 33^{\circ}) = (1 + 	an 12^{\circ})(1 + 	an 33^{\circ})$ $= 1 + 	an 33^{\circ} + 	an 12^{\circ} + 	an 12^{\circ} 	an 33^{\circ}$ Using the identity $	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$,we have $	an(12^{\circ} + 33^{\circ}) = 	an 45^{\circ} = 1$ $\Rightarrow \frac{	an 12^{\circ} + 	an 33^{\circ}}{1 - 	an 12^{\circ} 	an 33^{\circ}} = 1$ $\Rightarrow 	an 12^{\circ} + 	an 33^{\circ} = 1 - 	an 12^{\circ} 	an 33^{\circ}$ Substituting this into our expression: $= 1 + (1 - 	an 12^{\circ} 	an 33^{\circ}) + 	an 12^{\circ} 	an 33^{\circ}$ $= 1 + 1 = 2$

$(1 - \tan 348^{\circ})(1 + \cot 417^{\circ})$ is equal to

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