SOLUTION: If {{{tan(3x) tan (2x) = tan (pi/4)}}}, find the value of {{{sin(5x)}}}, given that {{{0 <= x <= pi/2}}}

Algebra ->  Trigonometry-basics -> SOLUTION: If {{{tan(3x) tan (2x) = tan (pi/4)}}}, find the value of {{{sin(5x)}}}, given that {{{0 <= x <= pi/2}}}      Log On


   

Question 1105386: If tan%283x%29+tan+%282x%29+=+tan+%28pi%2F4%29, find the value of sin%285x%29, given that 0+%3C=+x+%3C=+pi%2F2
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
If  tan(3x)*tan(2x) = tan%28pi%2F4%29,   then

    tan(3x)*tan(2x) = 1.


It implies that  3x + 2x = pi%2F2,   or

                 5x = pi%2F2.


Hence,  sin(5x) = sin%28pi%2F2%29 = 1.


Answer.  If  tan(3x)*tan(2x) = tan%28pi%2F4%29,  then  sin(5x) = 1.