The value of tan 57^{circ} - tan 12^{circ} - | vedclass

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Question

(A) We know the trigonometric identity for the tangent of a difference: $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$.Let $A = 57^{\circ}$

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) We know the trigonometric identity for the tangent of a difference: $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$.Let $A = 57^{\circ}$ and $B = 12^{\circ}$.Then,$	an(57^{\circ} - 12^{\circ}) = \frac{	an 57^{\circ} - 	an 12^{\circ}}{1 + 	an 57^{\circ} 	an 12^{\circ}}$.Since $57^{\circ} - 12^{\circ} = 45^{\circ}$,we have $	an 45^{\circ} = 1$.Therefore,$1 = \frac{	an 57^{\circ} - 	an 12^{\circ}}{1 + 	an 57^{\circ} 	an 12^{\circ}}$.Multiplying both sides by $(1 + 	an 57^{\circ} 	an 12^{\circ})$,we get:$1 + 	an 57^{\circ} 	an 12^{\circ} = 	an 57^{\circ} - 	an 12^{\circ}$.Rearranging the terms to match the given expression:$	an 57^{\circ} - 	an 12^{\circ} - 	an 57^{\circ} 	an 12^{\circ} = 1$.

The value of $\tan 57^{\circ} - \tan 12^{\circ} - \tan 57^{\circ} \tan 12^{\circ} =$ ?

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