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

Question 1190066: Please help me with this question, Given that tan(x) = a/b, 180° ≤ x ≤ 270°, evaluate cos(4x)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Given:

=> and

we will have real solution if
, , when ° ≤ ≤ °

use identity:

Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
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.

Given tan(x) = . It implies = , = . Use identity: cos(4x) = sin^4(x) + cos^4(x) - 6 sin^2(x) cos^2(x). It gives cos(4x) = + - (1) or cos(4x) = . (2) Any of formulas (1) or (2) is the ANSWER.

RELATED QUESTIONS
Use the given information to evaluate each expression. (Enter your answers in exact... (answered by ikleyn)
Please help me solve this question. A curve has the equation {{{y=acosbx+c}}} , with (answered by ikleyn)
Please help me find the equivalent to this expression. {{{ sin(-x)/cos(-x) }}} A.)... (answered by Edwin McCravy)
Please help me solve this question. A curve has the equation {{{y=acosbx+c}}} , with (answered by Theo)
Please help me solve this two part question: Given cos alpha= -4/5, 90 < alpha < 180... (answered by jim_thompson5910)
Hi, can someone help me in the 2nd part to find x. Question: By writing cos 4x = cos... (answered by josgarithmetic)
By considering a unit circle, decide whether the following are true or false: Sin 10<... (answered by Edwin McCravy)
please help me solve this question: Given that tan (x+y)=3 and tan (x-y)=1, find the... (answered by lwsshak3)
please could someone help me with this question. evaluate 2x^2 - 4x ____________... (answered by checkley77)