Sin(2*a) - tg(a) * ctg(a)

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вопрос

The expression can be simplified using trigonometric identities.

sin(2a) = 2sin(a)cos(a)
tan(a) = sin(a)/cos(a)
cot(a) = cos(a)/sin(a)

Substitute these identities into the expression:

2sin(a)cos(a) - (sin(a)/cos(a)) * (cos(a)/sin(a))

Simplify further:

2sin(a)cos(a) - sin^2(a)/cos(a)

= 2sin(a)cos(a) - sin^2(a)/cos(a)

= sin(a)(2cos(a) - sin(a))/cos(a)

Therefore, sin(2a) - tan(a)*cot(a) simplifies to sin(a)(2cos(a) - sin(a))/cos(a).