What is tan2θ1sin4θcsc2θ in terms of non-exponential trigonometric functions?

2 Answers
Aug 2, 2016

tan2θ1sin4θcsc2θ

=sin2θcos2θ1(1sin2θ)(1+sin2θ)csc2θ

=sin2θcos4θ11+sin2θcsc2θ

=8sin2θ(2cos2θ)212+2sin2θcsc2θ

=4(1cos2θ)(1+cos2θ)212+1cos2θcsc2θ

=8(1cos2θ)2+4cos2θ+2cos22θ13cos2θ22sin2θ

=8(1cos2θ)3+4cos2θ+cos4θ13cos2θ21cos2θ

Aug 2, 2016

tan2θ1sin4θcsc2θ

=sin2θcos2θ1(1sin2θ)(1+sin2θ)csc2θ

=sin2θcos4θ11+sin2θcsc2θ

=8sin2θ(2cos2θ)212+2sin2θcsc2θ

=4(1cos2θ)(1+cos2θ)212+1cos2θcsc2θ

=8(1cos2θ)2+4cos2θ+2cos22θ13cos2θ22sin2θ

=8(1cos2θ)3+4cos2θ+cos4θ13cos2θ21cos2θ