Homework Soursewhy does 1square root ofabcosx2bacosx2abcosx2All multiplyed
why does -1/square root of((a+bcosx)^2)-(b+acosx)^2)/(a+bcosx)^2...All multiplyed by ((b^2-a^x)(sinx))/(a+bcosx)^2....turn into -1/square root of (a^2-b^2)(1-cos^2x) all multiplyed by ((b^2-a^2)sinx)/(a+bcosx)...My question is where did the squared numerator g...is it because of the square root then you just move it to the numerator?
Solution
I\'m pretty sure that there\'s easier way to do this if you\'re taking DE class. But, If y = A sin + B cos, y\' = A cos - B sin y\'\' = -A sin - B cos Since y\'\' + y \' - 2y = sin, (-A sin - B cos) + (A cos - B sin) - 2(A sin + B cos) = sin iff (-A - B - 2A)sin + (-B + A - 2B)cos = sin Since there\'s only sin on the right side, coefficient of sin on the left side must be equal to 1 and that of cos must be equal to 0. So, -A - B - 2A = -3A - B = 1 and -B + A - 2B = A - 3B = 0 Solving the system of equation, A - 3B = 0 iff A = 3B -3A - B = 1 -3(3B) - B = 1 iff -9B -B = 1 iff -10B = 1 iff B = -1/10
