Match each expression in Column I with its equivalent expressi...

Question

Match each expression in Column I with its equivalent expression in Column II.

(tan (π/3) - tan (π/4))/(1 + tan (π/3) tan (π/4))

Accepted Answer

Hey, everyone. Here we are asked which of the following expressions is equivalent to tangent of pi divided by seven plus tangent of pi divided by four, all divided by one minus tangent of pi divided by seven multiplied by tangent of pi divided by four. Here we have four answer choice options. Answer choice A sine of 11 pi divided by 28. Answer B cosine of three pi divided by 28 answer C cosine of 11 pi divided by 28 and answer D tangent of 11 pi divided by 28. So to begin this problem, we first need to recall the sum identity for tangent functions. And so we have tangent of A plus B is equivalent to tangent of A plus tangent of B all divided by one minus tangent of a multiplied by tangent of B. And now we want to recall our given expression where we again have tangent of pi divided by seven plus tangent of pi divided by four all divided by one minus tangent of pi divided by seven multiplied by tangent of pi divided by four. And now comparing our formula to our given expression, we can notice that the right hand side of the formula is directly similar to the format of the given expression. And so we can simply compare the formula to our expression and determine our values for A and B. So comparing, we can notice that our value for A is pi divided by seven. And then our value for B is pi divided by four. And now utilizing the left hand side of the formula and our identified values, we can rewrite our given expression. And so instead of tangent of A plus B, in our case, we have tangent of pi divided by seven plus pi divided by four. And now that we have rewritten our given expression in its equivalent form, we just need to simplify the expression by summing our two fractions. And so we can notice that our fractions have different denominators. So we first need to, to find common denominators. And so in doing this, our expression becomes tangent of four pi divided by 28 plus seven pi divided by 28. And now that we have found common denominators, we can simply sum our numerators. And so we have tangent of 11 pi divided by 28. And with our final simplified answer, we are left here with answer choice D where again, we have tangent of 11 pi divided by 28. Thanks for watching. I hope you found this video helpful and I'll see you again next time

Match each expression in Column I with its equivalent expression in Column II.
(tan (π/3) - tan (π/4))/(1 + tan (π/3) tan (π/4))

Key Concepts

Tangent Function

Trigonometric Identities

Angle Measurement in Radians

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