To simplify the expression, let's first expand the terms:
(1 - sin α × cos α × tg α) + sin² α + = 1 - sin α cos α tg α + sin² α + 3
Now, we can use trigonometric identities to simplify further. The trigonometric identity we will use is:
sin² α + cos² α = 1
So, we can replace sin² α with (1 - cos² α):
1 - sin α cos α tg α + (1 - cos² α) + = 1 - sin α cos α tg α + 1 - cos² α + = 5 - sin α cos α tg α - cos² α
So, the simplified expression is:
5 - sin α cos α tg α - cos² α
To simplify the expression, let's first expand the terms:
(1 - sin α × cos α × tg α) + sin² α +
= 1 - sin α cos α tg α + sin² α + 3
Now, we can use trigonometric identities to simplify further. The trigonometric identity we will use is:
sin² α + cos² α = 1
So, we can replace sin² α with (1 - cos² α):
1 - sin α cos α tg α + (1 - cos² α) +
= 1 - sin α cos α tg α + 1 - cos² α +
= 5 - sin α cos α tg α - cos² α
So, the simplified expression is:
5 - sin α cos α tg α - cos² α