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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.