Question

Trigonometic Equations and Inequalities.
Solve the following equations
Does the equation 4 sin 2x + cos x = 5 have a solution?

Answer 1

given $4sin2x+cosx=5$

inorder the equation has a solution $sin2x$ and $cosx$ must be 1 at the same time since max value of sin and cos are 1

therefore cosx=1 at 0 but sin is 0 at 0, therefore, it has no solution