Question 910327
looks like your angle is going to be 30 degrees.


here's why:


start with 7 * sin^2(x) + 3 * cos^2(x) = 4


subtract cos^2(x) from both sides of the equation to get:


7 * sin^2(x) = -3 * cos^2(x) + 4


divide both sides of the equation by sin^2(x) to get:


7 * sin^2(x) / sin^2(x) = -3 * cos^2(x) / sin^2(x) + 4 / sin^2(x)


sin^2(x) / sin^2(x) = 1
cos^2(x) / sin^2(x) = cot^2(x)
1 / sin^2(x) = csc^2(x)


your equation becomes:


7 = -3 * cot^2(x) + 4 * csc^2(x)


since csc^2(x) is equal to 1 + cot^2(x), your equation becomes:


7 = -3 * cot^2(x) + 4 * (1 + cot^2(x))


simplify to get:


7 = -3 * cot^2(x) + 4 + 4 * cot^2(x)


subtract 4 from both sides of the equation to get:


3 = -3 * cot^2(x) + 4 * cot^2(x)


combine like terms to get:


3 = cot^2(x)


take the square root of both sides of the equation to get:


+/- sqrt(3) = cot(x)


you get:


cot(x) = sqrt(3) or cot(x) = -3


since tan(x) is equal to 1/cot(x), then you get:


1/tan(x) = sqrt(3) or 1/tan(x) = -sqrt(3)


solve for tan(x) and you get:


tan(x) = 1/sqrt(3) or tan(x) = -1/sqrt(3)


your solution is:


tan(x) = plus or minus 1 / sqrt(3)


if you need to rationalize the denominator, then your solution is:


tan(x) = plus or minus sqrt(3)/3