The number of distinct solutions of the equation 5 4 cos 2 ⁡   2 x + cos 4 ⁡ x + sin 4…

The number of distinct solutions of the equation 54cos2⁡ 2x+cos4⁡x+sin4⁡x+cos6⁡x+sin6⁡x=2 in the interval [0, 2π] is

Solution

54cos2⁡2x+sin2⁡x+cos2⁡x2+sin2⁡x+cos2⁡x3-5sin2⁡x.cos2⁡x=2
⇒541-sin2⁡2x-54sin2⁡2x+2=2
⇒1-2sin2⁡2x=0
⇒sin2⁡2x=12 
⇒2x=nπ±π4
⇒x=nπ2±π8
Number of solution = 8

Asked in: JEE Advanced 2015 (Paper 1)

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