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        the sum of all values of x belongs from 0 to 90 dedree satisfying sin2 2x+cos4 2x=3/4
8 months ago

Samyak Jain
333 Points
							x)2 = 3/42 cos2 2x + (2sinx = 3/4   $\dpi{100} \Rightarrow$  24 os 2x + c2sinsin2 2x + (1 – sin2 2x)2 = 3/4   $\dpi{100} \Rightarrow$  sin2 2x + 1 – 2 sin2 2x + sin4 2x  = 3/4or  sin4 2x – sin2 2x + 1/4 = 0  $\dpi{100} \Rightarrow$  (sin2 2x – 1/2)2 = 0i.e. sin2 2x = 1/2  =  (1/$\dpi{80} \small \sqrt{2}$)2   or   sin2 2x  =  sin2 $\dpi{100} \pi$/4$\dpi{100} \therefore$  2x = n$\dpi{100} \pi$ $\dpi{80} \pm$ $\dpi{100} \pi$/4  i.e.  x = n$\dpi{100} \pi$/2 $\dpi{80} \pm$ $\dpi{100} \pi$/8Put n=0, then x = $\dpi{100} \pi$/8  [$\dpi{80} \because$ x belongs to 0 to $\dpi{100} \pi$/2 or 90$\dpi{80} \degree$]Put n = 1, then x = $\dpi{100} \pi$/2 $\dpi{80} \pm$ $\dpi{100} \pi$/8  =  5$\dpi{100} \pi$/8  or  3$\dpi{100} \pi$/8  [x = 5$\dpi{100} \pi$/8 isn’t possible for x belongs to 0 to $\dpi{100} \pi$/2]Hence $\dpi{100} \pi$/8 and 3$\dpi{100} \pi$/8 are the required solutions whosesum = $\dpi{100} \pi$/8 + 3$\dpi{100} \pi$/8 = $\dpi{100} \pi$/2 or 90$\dpi{80} \degree$ .

8 months ago
Samyak Jain
333 Points
							  = 3/4x2 sin4 + x2 sin2sin2 2x + 1 – 2   $\dpi{100} \Rightarrow$= 3/4    2x + (1 – sin2 2x)2 2sin= ¾ 2x + (cos2 2x)2 2sinor  sin4 2x – sin2 2x + 1/4 = 0  $\dpi{100} \Rightarrow$  (sin2 2x – 1/2)2 = 0i.e. sin2 2x = 1/2  =  (1/$\dpi{80} \small \sqrt{2}$)2   or   sin2 2x  =  sin2 $\dpi{100} \pi$/4$\dpi{100} \therefore$  2x = n$\dpi{100} \pi$ $\dpi{80} \pm$ $\dpi{100} \pi$/4  i.e.  x = n$\dpi{100} \pi$/2 $\dpi{80} \pm$ $\dpi{100} \pi$/8Put n=0, then x = $\dpi{100} \pi$/8  [$\dpi{80} \because$ x belongs to 0 to $\dpi{100} \pi$/2 or 90$\dpi{80} \degree$]Put n = 1, then x = $\dpi{100} \pi$/2 $\dpi{80} \pm$ $\dpi{100} \pi$/8  =  5$\dpi{100} \pi$/8  or  3$\dpi{100} \pi$/8  [x = 5$\dpi{100} \pi$/8 isn’t possible for x belongs to 0 to $\dpi{100} \pi$/2]Hence $\dpi{100} \pi$/8 and 3$\dpi{100} \pi$/8 are the required solutions whosesum = $\dpi{100} \pi$/8 + 3$\dpi{100} \pi$/8 = $\dpi{100} \pi$/2 or 90$\dpi{80} \degree$ .

8 months ago
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• 31 Video Lectures
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• Test paper with Video Solution
• Mind Map
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