Question

15 cos^2x-15 если ctgx=2

Answer 1

Объяснение:

15cos²X-15 = 15(cos²X-1) = 15(-sin²X) = -15sin²X

Ток причем тут котангенс, - вообще не врубаюсь ¯\_(._. )_/¯

Answer 2

To find the value of the expression 15 cos^2(x) - 15 given that cot(x) = 2, we need to first determine the value of cos(x).

We know that cot(x) is the reciprocal of tan(x):

cot(x) = 1 / tan(x)

Since cot(x) = 2, we can rewrite it as:

2 = 1 / tan(x)

To find tan(x), we take the reciprocal of 2:

tan(x) = 1 / 2

Now, we can use the trigonometric identity:

tan^2(x) + 1 = sec^2(x)

Substitute tan(x) = 1/2 into the identity:

(1/2)^2 + 1 = sec^2(x)

1/4 + 1 = sec^2(x)

5/4 = sec^2(x)

Now, to find cos(x), we use the identity:

sec^2(x) = 1 / cos^2(x)

Substitute sec^2(x) = 5/4 into the identity:

1 / cos^2(x) = 5/4

To solve for cos^2(x), take the reciprocal of both sides:

cos^2(x) = 4/5

Finally, we can find the value of the expression 15 cos^2(x) - 15:

15 cos^2(x) - 15 = 15 * (4/5) - 15 = (60/5) - 15 = 12 - 15 = -3

So, the value of the expression is -3.