\(\frac{{{\rm{si}}{{\rm{n}}^6}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^6}{\rm{\theta }}}}{{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}\) is equal to -
\(\frac{{{\rm{si}}{{\rm{n}}^6}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^6}{\rm{\theta }}}}{{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}\) is equal to -
1). sin4θ - cos4θ
2). 1 - sin2θ cos2θ
3). 1 + sin2θ cos2θ
4). 1 - 3 sin2θ cos2θ
1 answers
$(\frac{{{\rm{si}}{{\rm{n}}^6}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^6}{\rm{\theta }}}}{{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}})$
$(= \frac{{{{\left( {{\rm{si}}{{\rm{n}}^2}{\rm{\theta }}} \right)}^3} - {{\left( {{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}} \right)}^3}}}{{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}})$
$(= \frac{{\left( {{\rm{si}}{{\rm{n}}^2}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}} \right)}}{{\left( {{\rm{si}}{{\rm{n}}^2}{\rm{\theta }} - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}} \right)}} \times \left( {{\rm{co}}{{\rm{s}}^4}{\rm{\theta }} + {\rm{si}}{{\rm{n}}^4}{\rm{\theta }} + {\rm{co}}{{\rm{s}}^2}{\rm{\theta si}}{{\rm{n}}^2}{\rm{\theta }}} \right))$
$(= {\rm{co}}{{\rm{s}}^4}{\rm{\theta }} + {\rm{si}}{{\rm{n}}^4}{\rm{\theta }} + {\rm{si}}{{\rm{n}}^2}{\rm{\theta co}}{{\rm{s}}^2}{\rm{\theta }})$
$(= 1 - 2{\rm{si}}{{\rm{n}}^2}{\rm{\theta co}}{{\rm{s}}^2}{\rm{\theta }} + {\rm{si}}{{\rm{n}}^2}{\rm{\theta co}}{{\rm{s}}^2}{\rm{\theta }})$
$(= 1 - {\rm{si}}{{\rm{n}}^2}{\rm{\theta co}}{{\rm{s}}^2}{\rm{\theta }})$
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