SOLUTION: tan(1/2cos^-1(6/7))

Question 1079196: tan(1/2cos^-1(6/7))
Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
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tan(1/2cos^-1(6/7))
~~~~~~~~~~~~~~~

We need to find tan(1/2cos^-1(6/7)), which is .

Let  = .


It means that  is the angle in QI such that  = .

And we need to find  = .


According to the formulas of half-angle 

    (they are basic formulas of Trigonometry; see the lesson Trigonometric functions of half argument in this site)


 =  =  =  = ,


 =  =  =  = .


Then   =  =  = .

Answer. tan(1/2cos^-1(6/7)) = = .

Solved.

If you want to see more solved problems of this kind, look into the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".

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