Question

Упростить:
1. (1 - $cos^{2}$ $alpha$ ) * (1 + $tg^{2}$ $alpha$ ) * $ctg^{2}$ $alpha$
2. (tg (90° - $alpha$ ) - ctg (90° + $alpha$ )² - (ctg (180° + $alpha$ ) + ctg (270° + $alpha$ ))²

Answer 1

1.
${ sin( alpha ) }^{2} times (1 + {( frac{ sin( alpha ) }{ cos( alpha ) } )}^{2} ) times { frac{ cos( alpha ) }{ sin( alpha ) } }^{2}$
${sin( alpha )}^{2} times (1 + frac{ {sin( alpha )}^{2} } { { cos( alpha ) }^{2} }) times frac{ { cos( alpha ) }^{2} }{ { sin( alpha ) }^{2} }$
sin²a сократим
$frac{{ cos( alpha ) }^{2} + { sin( alpha ) }^{2} }{ { cos( alpha ) }^{2} } times {cos( alpha )}^{2}$
cos²a+sin²a=1
cos²a сократим
$1$
2.
(tg a + ct²(90°+a)-tg a -ctg a)²=(-tg²a-1/tg a)²=(- tg³a+1/tg a)²=(tg³a+1)²/tg² a=tg^6 a+2tg³a+1/tg²a