Solve for positives solution

Question

Solve  for the first 2 positive solutions

Solve for the smallest positive solution.

Answer 1

-sin(x) + cos(5x) = √26 cos(x + atan(1/5))

Thus, -sin(x) + cos(5x) = 4 when x = acos(4/√26) - atan(1/5), 2 π - acos(4/√26) - atan(1/5)

These values are approximately .4716, 5.4168

sin(2x)cos(4x) - cos(2x)sin(4x) = sin(2x-4x) = sin(-2x) = - sin(2x)

-sin(2x) =-.25

x = 1/2 asin(1/4) = .1263