If tan(2x)=3/4, where x lies in the first quadrant, find the exact value of tan(6x)
Show answer & explanation
Correct answer: B
Explanation
tan(6x) = -117/44
Full work:
tan(2x) = 3/4
tan(6x) = (3tan(2x) - tan³(2x)) / (1 - 3tan²(2x))
= (3(3/4) - (3/4)³) / (1 - 3(3/4)²)
= (9/4 - 27/64) / (1 - 27/16)
= (117/64) / (-11/16)
= -117/44