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