Question

Cos (n + a ) tg ( a + п /2 ) =

Answer 1

Ответ:

cos(a)ctg(a)

Пошаговое объяснение:

cos(п+a)=-cos(a);

tg(a+п/2)=-ctg(a);

-cos(a)(-ctg(a))=cos(a)ctg(a)

Answer 2

To simplify this trigonometric expression, we can use some basic trigonometric identities and properties. The given expression is:

cos(n + a) * tan(a + π/2)

We know that:

1. tan(x) = sin(x) / cos(x)
2. tan(x + π/2) = -cot(x) = -1/tan(x) (since tan(x + π/2) = sin(x + π/2) / cos(x + π/2) and sin(x + π/2) = cos(x), cos(x + π/2) = -sin(x))
3. cos(n + a) = cos(n)cos(a) - sin(n)sin(a) (using the angle sum formula for cosine)

Now, we can rewrite the given expression using these identities:

cos(n + a) * tan(a + π/2) = (cos(n)cos(a) - sin(n)sin(a)) * (-1/tan(a))

Now, we substitute tan(a) = sin(a)/cos(a):

= (cos(n)cos(a) - sin(n)sin(a)) * (-1) * (cos(a) / sin(a))

We can rearrange the terms:

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

Now, we simplify the expression:

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

And that's the simplified form of the given expression:

cos(n + a) * tan(a + π/2) = -cos(n)cos^2(a) / sin(a) + sin(n)cos(a)