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If 4^(sin2x+2cos^2 x) +4^(1-sin2x+2sin^2 x) =65 then sin2x + cos2x has the value equal to

If 4^(sin2x+2cos^2 x) +4^(1-sin2x+2sin^2 x) =65 then sin2x + cos2x has the value equal to

Grade:12th pass

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
we can get 65 by 64+1 so
either
1-sin2x+2sin2x = 0 or sin2x+2cos2x=0\
sin2x+cos2x = -1
sin(2x+pie/4) = -1
so 2x+pie/4 =npie+(-1)n 5pie/4 find x from here
Anish Singhal
askIITians Faculty 1192 Points
5 years ago
If u assume the value of(sin2x+2cos^2 x) as 3 then the factor(1-sin2x+2sin^2 x) will have value 0.
Hence by taking value of(sin2x+2cos^2 x) as 3 simplify and find the value of sin2x+cos2x

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