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(sin(2*theta) %2B sin(4*theta))/(cos(4*theta) %2B 1 %2B cos(2*theta))=(2*tan(theta))/(-tan(theta)^2 %2B 1) |
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Answer» sin4x+ sin2x= sim2x+2sinxcosx= sin2x(1+2cos2x)=sin4x=2sinxcosx for the denomater 1+ cos2x+ cos4x; using cos2theta= cos^(2)theta- sin^(2)theta= 2 cos^(2)theta-2; we substitute cos4x as 2cos^(2)2x -1, so, 1cos2x+ cps4x=1+ cos2x + 2cos^(2)2x-1= cos3x+2 cos^(2)2x, I,e. cos2x(1+2cos2x), so the numerator and demonator now have a common factor as (1+2 cos2x), so dividing we sin2x/ cos2x left which is equivalent to which is equivalent to tan2x |
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