Question

Answer please. i need help

Answer 1

Answer:

Option 2

Step-by-step explanation:

2sin²x + cos(2x) - 2 < -1

2sin²x + (1 - 2sin²x) - 2 < -1

2sin²x + 1 - 2sin²x - 2 + 1 < 0

0 < 0

Is a false statement

Answer 2

Answer:

B

Step-by-step explanation:

For this problem, it would be wise to actually graph the two equations on a graphing calculator.

Doing so, you see that, indeed, both the graph $y=2(sin(x))^{2} + cos(2x) - 2$ and $y = -1$ are the same.

However, looking back at the original problem, we see that we're looking for solutions where  $y=2(sin(x))^{2} + cos(2x) - 2$ is less than $y = -1$. Since the graph shows that all the solutions of the first equation are the solutions for the second equation, as well, there are NO solutions that make the first equation smaller than the second.

Hence, the answer is (b) because it is the only one that gives the correct answer and explanation.