Question

√10ctga×sin(a+Π),если cisa=√10/4

Answer 1

Решение задания смотри на фотографии

Answer 2

To simplify the expression √10ctga×sin(a+Π), let's start by expressing the trigonometric functions in terms of the given value of cisa.

Given: cisa = √10/4

We know that: cot(a) = 1/tan(a)

cot(a) = 1/cisa (since cisa = √10/4)

cot(a) = 1/(√10/4)

Now, let's simplify cot(a):

cot(a) = 4/√10

Now, we can rewrite the expression:

√10ctga×sin(a+Π)

Since cot(a) = 4/√10, we can replace ctga with 4/√10:

√10 * (4/√10) * sin(a+Π)

The √10 in the numerator and denominator cancels out:

(4/√10) * sin(a+Π)

Now, sin(a+Π) can be rewritten as sin(a) since sin(x+Π) = -sin(x):

(4/√10) * (-sin(a))

Finally, we simplify the expression:

-4√10 * sin(a)

So, √10ctga×sin(a+Π) with cisa = √10/4 is equal to -4√10 * sin(a).