Question

The solution set if sin(3x) + cos (3x) = -2​

Answer 1

Answer:

Null set

Step-by-step explanation:

There is no solution because

-√2 <= sin(3x) +cos(3x) <=√2

but -2 is out of range.

Answer 2

Answer:

    Empty!   I.e. there are no solutions.

Step-by-step explanation:

Since the minimum value of sin(x) and cos(x) is -1, it follows that

   sin(3x) + cos(3x)  ≥  -2

for all values of x, and the only way to get equality would be to have

   sin(3x) = cos(3x) = -1.

But

   cos(3x) = -1  ⇒  3x = nπ, where n is an odd integer,

and

   sin(3x) = -1  ⇒  3x = (n + 1/2)π, where n is an odd integer.

In particular, they cannot both be -1 at the same time, so their sum can never be equal to -2.