(cosx / sinx) + (2sinx / cosx) + (sin^3x / cos^3x) How to simplify the expression with the LCM?
The LCM is sinx*cos^3x....so we have
cos(x) cos^3 (x) / [ sin (x) * cos^3 (x)] +
[2 sinx * sin x * cos^2 (x)] / [sin (x)cos^3 (x)] +
[ sin (x) sin^3(x)] / [ sin(x) cos^3 (x) ] =
[cos^4 (x) + 2 sin (x) cos^3(x) + sin^4 (x)] / [ sin (x)cos^3(x) ] =
[cos^4 (x) + 2 sin (x) cos(x) * cos^2(x) + sin^4 (x)] / [ sin (x)cos^3(x) ] =
[ cos^4 (x) + sin(2x)*cos^2(x) + sin^4(x) ] / [ sin(x)cos^3(x) ]
(cosx / sinx) + (2sinx / cosx) + (sin^3x / cos^3x)
How to simplify the expression with the LCM?
cos(x)sin(x)+2sin(x)cos(x)+sin3(x)cos3(x)=cos(x)sin(x)⋅cos3(x)cos3(x)+2sin(x)cos(x)⋅sin(x)cos2(x)sin(x)cos2(x)+sin3(x)cos3(x)⋅sin(x)sin(x)=cos(x)cos3(x)+2sin(x)sin(x)cos2(x)+sin3(x)sin(x)sin(x)cos3(x)=cos4(x)+2sin2(x)cos2(x)+sin4(x)sin(x)cos3(x)=sin4(x)+2sin2(x)cos2(x)+cos4(x)sin(x)cos3(x)=(sin2(x)+cos2(x))2sin(x)cos3(x)|sin2(x)+cos2(x)=1=12sin(x)cos3(x)=1sin(x)cos3(x)