Using the difference for formula, find the tan 255.
Step by step would be appreciated
To find the tangent of 255, you can use the tangent difference formula, which states that tan(A + B) = [tan(A) + tan(B)] / [1 - tan(A) * tan(B)]. In this case, we want to find tan(255), so we'll use A = 240 and B = 15, where A = a multiple of 45 degrees and B = the difference between 255 and the closest multiple of 45 degrees, which is 240.
Step 1: Find tan(A) and tan(B)
You can use a scientific calculator or reference tables to find the tangent of 240 and 15 degrees.
tan(240) ≈ -1.732
tan(15) ≈ 0.267
Step 2: Substitute the values into the formula
tan(255) = [tan(240) + tan(15)] / [1 - tan(240) * tan(15)]
= (-1.732 + 0.267) / (1 - (-1.732 * 0.267))
= -1.465 / (1 + 0.461)
= -1.465 / 1.461
≈ -1.003
Therefore, tan(255) is approximately -1.003.
tan(255) = tan(180+75) = tan 75 = tan(30 + 45)
= (tan30+tan45)/ (1-tan30tan45)
You can finish the rest.
Note:
tan(180+75) = (tan180+tan75)/ (1-tan180tan75)
= (0+ tan75)/(1-0)
=tan 75
= tan (30+45)
not my answer but credits to: mlam18