Question

Ctg a · tg a - cos² a 2 cos2α sin2a sin a cos a

Answer 1

Ctg a · tg a=11-cos² a=sina

Answer 2

I will try to answer your question in detail. You want to simplify the expression Ctg a · tg a - cos² a 2 cos2α sin2a sin a cos a.

First, let's rewrite the expression using some trigonometric identities:

Ctg a · tg a - cos² a 2 cos2α sin2a sin a cos a = (cos a / sin a) · (sin a / cos a) - cos² a 2 (cos (2α)) (sin (2a)) sin a cos a

= 1 - cos² a 2 (cos² α - sin² α) (2 sin a cos a) sin a cos a

= 1 - cos² a 2 (cos² α - sin² α) (sin (2a)) sin a cos a

Now, let's simplify the expression by canceling out some common factors:

1 - cos² a 2 (cos² α - sin² α) (sin (2a)) sin a cos a = (1 - cos² a) / (2 cos² α - 2 sin² α) sin (2a)

= (sin² a) / (cos (2α)) sin (2a)

= (sin a)² / (cos (2α) sin (2a))

This is the final simplified form of the expression. You can check the validity of this result using an online calculator or by substituting some values for a and α. I hope this helps you understand the process of simplifying trigonometric expressions. If you have any further questions, please feel free to ask me.