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Evaluate Tan 13π/12 |
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Answer» Tu ki laina pdhla apna By the tangent subtraction formula: tan(A - B) = [tan(A) - tan(B)]/[1 + tan(A)tan(B)]. Thus: tan(13π/12) = tan(4π/3 - π/4), from the hint = [tan(4π/3) - tan(π/4)]/[1 + tan(4π/3)tan(π/4)], from the above formula = (-1 + √3)/(1 + √3) = -(1 - √3)/(1 + √3) = -(1 - √3)^2/[(1 + √3)(1 - √3)], by rationalizing = -(1 - √3)^2/(1 - 3), via difference of squares = (1/2)(1 - √3)^2 = (1/2)(1 - 2√3 + 3) = (1/2)(4 - 2√3) = 2 - √3. |
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