Question

3cos^2a-5sin^2a=? Tga=5

Answer 1

Ответ:

Объяснение:

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Answer 2

Ответ: во вложении Объяснение:

Answer 3

To find the value of the expression 3cos^2(a) - 5sin^2(a) and the value of tg(a) when tg(a) = 5, we first need to determine the values of cosine and sine functions at angle 'a'. Then, we can substitute those values into the expressions.

Let's start with the value of tg(a) = 5. The tangent function (tg or tan) of an angle 'a' is defined as the ratio of the sine to the cosine of that angle. So, we have:

tg(a) = sin(a) / cos(a)

Since tg(a) = 5, we can set up the following equation:

5 = sin(a) / cos(a)

Now, let's find the value of cos(a). We can rearrange the equation to solve for cos(a):

cos(a) = sin(a) / 5

Next, we can use the trigonometric identity: sin^2(a) + cos^2(a) = 1

Substitute the expression we just found for cos(a) into the identity:

sin^2(a) + (sin(a) / 5)^2 = 1

Expand and simplify:

sin^2(a) + sin^2(a) / 25 = 1

Multiply through by 25 to get rid of the fraction:

25 * sin^2(a) + sin^2(a) = 25

Combine like terms:

26 * sin^2(a) = 25

Now, solve for sin(a):

sin^2(a) = 25 / 26

sin(a) = sqrt(25 / 26)

Now, find the value of cos(a) using the previously found value for sin(a):

cos(a) = sin(a) / 5

cos(a) = sqrt(25 / 26) / 5

Now, we have the values of sin(a) and cos(a). We can calculate the expression 3cos^2(a) - 5sin^2(a):

3cos^2(a) - 5sin^2(a) = 3 * (sqrt(25 / 26) / 5)^2 - 5 * (sqrt(25 / 26))^2

Simplify further:

3 * (25 / 26) / 25 - 5 * (25 / 26)

Cancel out the common factors:

3 / 26 - 125 / 26

Combine the terms:

(3 - 125) / 26 = -122 / 26 = -61 / 13

So, 3cos^2(a) - 5sin^2(a) is equal to -61 / 13.