Question

Anybody can do this
if tanβ+cotβ=2,
then find (secβ)^2-(cosecβ)^2

Answer 1

$\tan( \beta ) = \binom{1 \ }{ \cot( \beta ) }$
given
$\binom{1}{cot \beta } + \cot( \beta ) = 2$

now taking lcm
$\binom{1 + \cot^{2} \beta }{ \cot( \beta ) } = 2$



using identity
$(1 + \cot^{2} \beta ) = \csc ^{2} ( \beta )$
now ,
$\binom{ \csc {}^{2} ( \beta ) }{ \cot( \beta ) } = 2$

now see the twist sec× cosec=2
sec beta =2/cosec beta
so now finally putting values