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Find the value of tan (a + pi/3)

Question:

If tan (a + b) = 1/3 and tan (b - pi/3) = 1/5, find the value of tan (a + pi/3) = ?

Solution:

tan ( a + pi/3)
= tan [(a + b) - (b - pi/3)]

Using the formula: tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

tan [(a + b) - (b - pi/3)]
= [tan (a + b) - tan (b - pi/3)]/[ 1 + tan (a + b) tan (b - pi/3)]
= (1/3 - 1/5)/[1 + (1/3) (1/5)]
= [(1 × 5)/(3 × 5) - (1 × 3)/(5 × 3)/[1 + (1/3) (1/5)]
= (5 - 3)/15 ÷ (15/15 + 1/15)
= 2/15 ÷ 16/15
= 2/15 × 15/16
= 2/16
= 1/8

Therefore, the value of tan ( a + pi/3) is 1/8. Watch the video for more details.