Multiple choice general knowledge math & puzzles

If tan2x=4root(2)/7 then sin(x)=?

  1. 1/2

  2. 1/root(2)

  3. 1/3

  4. 1/root(3)

  5. root(3)/2

  6. none of above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If tan(2x) = 4sqrt(2)/7, use tan(2x) = 2tan(x)/(1-tan²x) to find tan(x) = sqrt(2)/4. Then sin(x) = tan(x)/sqrt(1+tan²x). Calculation: sin(x) = (sqrt(2)/4) / sqrt(1 + 2/16) = (sqrt(2)/4) / (3/sqrt(8)) = (sqrt(2)/4) * (2sqrt(2)/3) = 4/12 = 1/3.

Keep practicing — related questions