Quote:
Originally Posted by MAS1
Wow, these are tough problems the way you have presented them. Maybe you have left out some parentheses or something.
For the 1st one, I am assuming that first dash is NOT a negative sign, therefore:
sinx*sqrt(2) = 2sinxcosx
sqrt(2) = 2cosx
sqrt(2)/2 = cosx
Taking the inverse cos of both sides gives
x = pi/4 and 7*pi/4
If the first dash is a negative sign, then x = 3*pi/4 and 5*pi/4.
Your solution is incorrect because 2sinxcosx = sin2x, not 2sinx.

I see you edited your equations.
For the second one:
2cosx  3/cosx + 2*sqrt(2) = 0
cosx*[2cosx  3/cosx + 2*sqrt(2)] = cosx*0
2(cosx)(cosx) + 2sqrt(2)*cosx  3 = 0
Using quadratic formula to solve for cosx gives:
cosx = sqrt(2)/2 and cosx = 3*sqrt(2)/2
For the 1st solution x = pi/4 and 7*pi/4
For the 2nd solution x = arccos(3*sqrt(2)/2)
Sorry, I don't have a calculator with trig functions on it for the second solution.
MAS1