Question

The number of distinct solutions of the equation
5/4 cos²2x + cos⁴x + sin⁴x + cos⁶x + sin⁶x = 2
in the interval [0, 2????] is

Answer 1

Step-by-step explanation:

Answer. = 8

        54cos2 2x + cos4 x+ sin4 x+cos6 x + sin6 x =254cos2⁡ 2x + cos4⁡ x+ sin4⁡ x+cos6⁡ x + sin6⁡ x =2

         54cos2 2x +(cos2 x+ sin2 x)2−2cos2 x sin2 x+(cos2 x+ sin2 x)3−3cos2 x sin2 x =254cos2⁡ 2x +(cos2⁡ x+ sin2⁡ x)2−2cos2⁡ x sin2⁡ x+(cos2⁡ x+ sin2⁡ x)3−3cos2⁡ x sin2⁡ x =2

         54cos2 2x +1− sin2 2x2 +1−34sin2 x =254cos2⁡ 2x +1− sin2⁡ 2x2 +1−34sin2⁡ x =2

          54cos2 2x −54

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Answer 2

Answer:

8

Step-by-step explanation: