Question

50 POINTS PLS HELP ASAP

Determine all solutions to the equation radical 2 times sine 2 times x equals sine squared x plus cosine squared x on the interval [0, 2π). (2 points)


a. x equals pi over 4 comma 3 times pi over 4
b. x equals pi over 4 comma 3 times pi over 4 comma 5 times pi over 4 comma 7 times pi over 4
c.x equals pi over 8 comma 3 times pi over 8
d. x equals pi over 8 comma 3 times pi over 8 comma 9 times pi over 8 comma 11 times pi over 8

Answer 1

Answer
Given
The equation,
V2 cos 2% = sin? « + cos? a

To determine all the solutions in the interval [0, 21).
Step-by-step explanation:
It is given that,
V2 cos 2.0 = sin? a + cOs? g
Since sin
(2 a + cos? g = 1

Then,
V2 cos 2% = sin? a + cos? g
÷ cos 2. =
1
v2
# 2. = cos 1(
+24=
Hence, the solutions of the given equation in [0, 2m) is,
(0) 2= 품, 품, 뜸, 뚱