Ctg2a-cos2a/tg2a-sin2a

Предыдущий
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вопрос

To simplify the given expression:

ctg(2a) - cos(2a) / tg(2a) - sin(2a)

First, we will use the double angle identities to simplify cosine and sine terms:

ctg(2a) - cos(2a) / tg(2a) - sin(2a)
= ctg(2a) - (cos^2(a) - sin^2(a)) / tg(2a) - 2sin(a)cos(a)
= ctg(2a) - cos^2(a) + sin^2(a) / tg(2a) - 2sin(a)cos(a)

Next, we will use the fact that the cotangent function is the reciprocal of the tangent function, and the Pythagorean trigonometric identity:

= 1/tg(2a) - (1 - sin^2(a)) / tg(2a) - 2sin(a)cos(a)
= 1/tg(2a) - cos^2(a) / tg(2a) - 2sin(a)cos(a)

Now, we will replace the tangent and cotangent functions with sine and cosine functions:

= 1/(sin(2a)/cos(2a)) - cos^2(a) / (sin(2a)/cos(2a)) - 2sin(a)cos(a)
= cos(2a)/sin(2a) - cos^2(a) / sin(2a)/cos(2a) - 2sin(a)cos(a)
= cos^2(a) - cos^2(a) / sin^2(a) - 2sin(a)cos(a)
= 0 / sin^2(a) - 2sin(a)cos(a)
= 0 / sin(2a)
= 0

Therefore, the simplified expression is 0.