If A + C = B, then tan A tan B tan C = | vedclass

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Question

(B) Given the relation $A + C = B.$Taking the tangent on both sides,we get $	an(A + C) = 	an B.$Using the trigonometric identity $	an(A + C) = \fra

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$	an B - 	an C - 	an A$

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(B) Given the relation $A + C = B.$Taking the tangent on both sides,we get $	an(A + C) = 	an B.$Using the trigonometric identity $	an(A + C) = \frac{	an A + 	an C}{1 - 	an A 	an C},$we have $\frac{	an A + 	an C}{1 - 	an A 	an C} = 	an B.$Cross-multiplying gives $	an A + 	an C = 	an B(1 - 	an A 	an C).$Expanding the right side,we get $	an A + 	an C = 	an B - 	an A 	an B 	an C.$Rearranging the terms to solve for $	an A 	an B 	an C,$we obtain $	an A 	an B 	an C = 	an B - 	an A - 	an C.$

If $A + C = B,$ then $\tan A \tan B \tan C = $

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