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Answer on Trigonometry Question for Isha
Question #1755
Solve this trigonometric equation.give all positive values of the angle between 0deg and 360deg that will satisfy.<br>Give any approximate value to the nearest minute only.
<br>& tan (x+15) = 3 tanx
<br>& tan (x+15) = 3 tanx
Expert's answer
Answer
tan(x+15) = (tanx + tan15)/(1tanx tan15)(tanx + tan15)/(1tanx tan15) = 3 tanx
tanx + tan 15 = 3 tanx  3tan2x tan15
3 tan^{2}x tan15  2tanx + tan15 = 0
tan15 = 0.27, denote tanx as t
0.81 t^{2 } 2t + 0.27 = 0
D = 0.1252
t_{1} = 1.67
t_{2 }= 0.80
tan (x_{1}) = 1.67
x_{1} = arctan (1.67) + πn = 59.087 + 180n = 59º 5'+ 180n, n=0,1,2,..
tan(x_{2}) = 0.80
x_{2} = arctan(0.80) + πn = 38.66 + 180n = 38º 40' + 180n, n=0,1,2,..
Answer: 59º 5', 239º 5', 38º 40', 218º 40'
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