Homework SourseSolve the following equations given that 0
Solve the following equations given that 0 <= x < 2 pi. Give exact answers whenever possible.
a) 1 + sin(x)^2 = 3sinxcosx
b) 4cos(x)^2 + sec(x)^2= 5
a) 1 + sin(x)^2 = 3sinxcosx
b) 4cos(x)^2 + sec(x)^2= 5
Solution
a) 1 + sinx^2 = 3sinxcosx = 1.5sin2x 1 + (1-cos2x)/2 = 1.5sin2x 1.5 - 0.5cos2x = 1.5sin2x x = pi/4 = 0.785 b) 4cosx^2 + secx^2 = 5 cosx = 1 or -1 x = 0,pi,2pi = 0,3.142,6.284
