Question

what is the value of the following

$\frac{ \ { \tan(x) }^{3} }{1 + { \tan(x) }^{2} } + \frac{ \cot(x) ^{3} }{1 + { \cot(x) }^{2} }$
let x= theta ​

Answer 1

Step-by-step explanation:

tanx³/1+tan² + cot³/1+cot²

=tan³x/sec²x + cot²x/cosec²x

=sin³x/cos³x × cos²x+cos³x/sin³x × sin²x

=sin³x/cosx+cos³x/sinx

=sin⁴x+cos⁴x/sinxcosx

=(sin²x+cos²x)²-2sin²xcos²x/sinxcosx

=1-2sin²xcos²x/sinxcosx

=cosecxsecx-2sinxcosx