Question

Example 12 Solve sin 3x + cos2x =-2.​

Answer 1

Answer:

If the sum of two quantities is -2 each of which cannot be less than -1, then each of them equals -1. Now sin 3x = -1 = sin 3π/2, gives x=nπ/3 +(-1)^n.π/2, i.e. π/3 - π/2, 2π/3 + π/2,…Similarly cos 2x =-1 =cos π gives x=nπ(+/-)π/2. The common values of the above two sets are the solutions required, of which the one nearest to 0 is π/2.