Question 1190066
.
Please help me with this question, Given that tan(x) = a/b, 180° ≤ x ≤ 270°, evaluate cos(4x)
~~~~~~~~~~~~~~~~~



            In the post by @MathLover1,  there are mistakes that lead to incorrect answer.


            I came to bring a correct solution.



<pre>
Given  tan(x) = {{{a/b}}}.


It implies  {{{sin^2(x)}}} = {{{a^2/(a^2+b^2)}}},  {{{cos^2(x)}}} = {{{b^2/(a^2+b^2)}}}.


Use identity:    cos(4x) = sin^4(x) + cos^4(x) - 6 sin^2(x) cos^2(x).


It gives


        cos(4x) = {{{a^4/(a^2+b^2)^2}}} + {{{b^4/(a^2+b^2)^2}}} - {{{(6a^2*b^2)/(a^2+b^2)^2}}}     (1)

    or  

        cos(4x) = {{{(a^4+b^4-6a^2*b^2)/(a^2+b^2)^2}}}.     (2)


Any of formulas (1) or (2) is the <U>ANSWER</U>.
</pre>