Question

0,8+4sin2(x)+cos(2x) если ctgx=3

Answer 1

Ответ:

Объяснение:1) сtgx=3⇒tgx=1/3.

2)cos2x=1-2sin²x,а 1+ctg²x=1/sin²x⇒sin²x=1/(1+ctg²x)=1:(1+3²)=1/10,значит

cos2x=1-2·1/10=1- 0,2=0,8.

3)sin2x=2tgx/(1+tg²x), sin2x=2·1/3 :(1+1/9)=2/3:10/9=6/10=0,6.

4)получим,0,8+4·0,6+0,8=1,6+2,4=4.

Answer 2

To find the value of the expression 0.8 + 4sin^2(x) + cos(2x) given that cot(x) = 3, we can start by using the given information to find the values of sin(x) and cos(x).

cot(x) = 3 Since cot(x) = 1/tan(x), we can rewrite it as: 1/tan(x) = 3

Taking the reciprocal of both sides: tan(x) = 1/3

Using the identity tan^2(x) + 1 = sec^2(x), we can find the value of sec(x): tan^2(x) + 1 = sec^2(x) (1/3)^2 + 1 = sec^2(x) 1/9 + 1 = sec^2(x) 10/9 = sec^2(x)

Taking the square root of both sides: sqrt(10/9) = sec(x) sqrt(10)/3 = sec(x)

Since sec(x) = 1/cos(x), we have: 1/cos(x) = sqrt(10)/3

Multiplying both sides by cos(x): 1 = sqrt(10)/3 * cos(x)

Simplifying: cos(x) = 3/sqrt(10)

Now, we can use the values of sin(x) and cos(x) to find the value of the given expression:

0.8 + 4sin^2(x) + cos(2x)

Since cos(2x) = 1 - 2sin^2(x), we can substitute the values: 0.8 + 4sin^2(x) + 1 - 2sin^2(x)

Simplifying: 0.8 + 2sin^2(x) + 1 = 1.8 + 2sin^2(x)

Now, we need to find the value of sin^2(x):

sin^2(x) = 1 - cos^2(x) = 1 - (3/sqrt(10))^2 = 1 - 9/10 = 1/10

Substituting this value back into the expression: 1.8 + 2 * (1/10) = 1.8 + 2/10 = 1.8 + 0.2 = 2

Therefore, the value of the expression 0.8 + 4sin^2(x) + cos(2x), when cot(x) = 3, is 2.