Question 697348
Solution :

1. {{{tan^2 (20)- sec^2 (20) }}}
{{{ (sin^2 (20) - 1)/cos^2 (20)}}}
{{{-cos^2 (20) / cos^2 (20) = -1}}}

2. {{{cos^2(10 degree 5`) + sin^2 (10 degree 5`)}}}
let 10 degree 5 = t
therefore, the equation becomes
{{{cos^2 (t) + sin^2 (t) = 1 }}}

3. {{{2sec^2 (2pie/7) cos^2 (2pie/7)}}}
let 2pie/7 = t
therefore, the equation becomes
{{{2sec^2 (t) * cos^2 (t)}}}
={{{ (2/cos^2 (t)) * cos^2 (t)}}}
 because sec (t) = 1/cos (t)
{{{2}}}