Question

5tg^2x*cos^2x+5sin^2*x*ctg^2x

Answer 1

Если я правильно поняла расположение всех знаков, то:

 

 5sin²x * cos²x       5sin²x * cos²x

--------------------- + ---------------------  =  5sin²x + 5cos²x =   5(sin²x + cos²x) = 5 * 1=5

cos²x                           sin²x

Answer 2

It looks like you have an expression that involves trigonometric functions. To simplify the expression, you can use trigonometric identities. In this case, you can use the following identities:

1. cot(x) = 1/tan(x)
2. tan(x) = sin(x)/cos(x)
3. sin^2(x) + cos^2(x) = 1

Using these identities, you can simplify your expression as follows:

5tan^2(x)cos^2(x) + 5sin^2(x)cot^2(x)

Now, replace cot^2(x) with 1/tan^2(x):

5tan^2(x)cos^2(x) + 5sin^2(x)(1/tan^2(x))

Next, you can distribute the 5sin^2(x) into the two terms:

5tan^2(x)cos^2(x) + 5sin^2(x)/tan^2(x)

Now, use the identity tan(x) = sin(x)/cos(x) to simplify the expression further:

5(sin^2(x)/cos^2(x))cos^2(x) + 5sin^2(x)/tan^2(x)

The cos^2(x) in the first term cancels out with one of the cos^2(x) in the denominator of the second term:

5sin^2(x) + 5sin^2(x)/tan^2(x)

Now, common denominator for the two terms is tan^2(x):

(5sin^2(x)tan^2(x) + 5sin^2(x))/tan^2(x)

Now, you can factor out a common factor of 5sin^2(x):

5sin^2(x)(tan^2(x) + 1)/tan^2(x)

Finally, simplify the expression further by using the identity tan^2(x) + 1 = sec^2(x):

5sin^2(x)sec^2(x)/tan^2(x)

So, the simplified expression is:

5sin^2(x)sec^2(x)/tan^2(x)