Expert: Ahmed Salami - 1/27/2009

Question
root of 3 * sinx = cosx ...

Answer
Hi Faisal,
(cosx)^2 + (sinx)^2 = 1
cosx = sqrt[1 - (sinx)^2]
So,
sqrt3.sinx = cosx
sqrt3.sinx = sqrt[1 - (sinx)^2]
squaring both sides,
3(sinx)^2 = 1 - (sinx)^2
4(sinx)^2 = 1
(sinx)^2 = 1/4
sinx = 1/2 OR -1/2
x = pi/6 or 5pi/6 OR 7pi/6 or 11pi/6
But, sinx and cosx should have the same sign according to the equation and that only happens when 0 < x < pi/2. We therefore take
x = pi/6  (30 degrees)

Regards