Find tan(22.5^(@)) using the half-angle formula.

Daisy Hatfield

Daisy Hatfield

Answered question


Find tan22.5 using the half-angle formula.

Answer & Explanation



Beginner2023-03-27Added 4 answers

Using the half-angle formula, determine the value.
We know that tan(2x)=2tanx1-tan(x)2 and
Let y=tan(x) where x=22.5
So 2x=45
Given that tan(45)=1
So 2y1-y2=1
We know if α and β are the roots of a quadratic equation of the form ax2+bx+c=0 then the roots are
Thus the roots are 2-1 and -2-1
Since, tan22.5 lie in first quadrant so we will take the positive value.
Thus, the value of tan22.5is 2-1

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