cos( α+ π) + sin ( α- 3π/2) - ctg( π/2 + α)*tg( 3π/2 + α)=? sin 420+ cos(-390) +...

Question

cos( α+ π) + sin ( α- 3π/2) - ctg( π/2 + α)*tg( 3π/2 + α)=?

sin 420+ cos(-390) + tg(-1230) - ctg420=?

sin 5π /18*cos π /9 - sin π/9 * cos 5 π/ 18 =?

tg² α + sin²α - 1/ cos²α=?

Answer 1

1) ... = -cos a + cos a + tg a*(-ctg a)= - ctg a*tg a = -1
2) .... = sin 60 - cos 30 - tg 150 - ctg 60 = sin 60 - cos 30 - tg (180 - 30) - ctg 60 =  kor3/2 - kor3/2 + kor3/3 - kor3/3 = 0

 

Answer 2

 = -cos a + cos a + tg a*(-ctg a)= - ctg a*tg a = -1

 = sin 60 - cos 30 - tg 150 - ctg 60 = sin 60 - cos 30 - tg (180 - 30) - ctg 60 =  kor3/2 - kor3/2 + kor3/3 - kor3/3 = 0