The required value of tan(7π/12) = √[(2+√3)/(2-√3)].
To find the exact value of tan(7π/12).
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
[tex]tanx =\sqrt{ \frac{1 -cos2x}{1 + cos2x} }[/tex]
tan(7π/12) = √ [ (1 - cos2(7π/12) ) / (1 + cos2(7π/12) ]
= √ [ (1 - cos(7π/6) ) / (1 + cos(7π/6) ]
= √ [ (1 - cos(π + π/6) ) / (1 + cos(π + π/6) ]
Since cos(π + x) = -cosx
= √ [ (1 + cos(π/6) ) / (1 - cos(π/6) ]
Here, cos( π/6 ) = √3/2
= √ [ (1 + √3/2 ) / (1 - √3/2 ]
= √ [ (2 + √3)/2 / (2- √3)/2 ]
= √ [ (2 + √3) / (2- √3) ]
Thus, the required value of tan (7π/12) = √ [ (2+√3)/(2-√3) ].
Learn more about trigonometry equations here:
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