Question

prove that:
1+sec0-tan0/tan0/1+sec0+tan0 = 1-sin0/cos0
​

Answer 1

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 2

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 3

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 4

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 5

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 6

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 7

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS

Answer 8

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

LHS=sin0-cos0+1/sin0+cos0-1

on dividing by cos0 up and down,then

tan0+se0-1/tan0-sec0+1

= sec0+tan0-(sec20-tan20)/tan0-sec0+1

= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1

=sec0+tan0(1-sec0+tan0)/tan0-sec0+1

=sec0+tan0*(sec0-tan0)/(sec0-tan0)

=(sec20-tan20)/(sec0-tan0)

=1/sec0-tan0)

=RHS