Question

2sina+5cosa/3cosa-sina, если tga=2

Answer 1

Ответ:

Найдите значение тригонометр.выражения.

Answer 2

To simplify the given expression, we can use the trigonometric identity:

tan(a) = sin(a) / cos(a)

Given that tan(a) = 2, we can substitute this value into the expression:

2sin(a) + 5cos(a) / (3cos(a) - sin(a))

Using the identity tan(a) = sin(a) / cos(a), we can rewrite the expression:

2tan(a)cos(a) + 5cos(a) / (3cos(a) - sin(a))

Now, substitute tan(a) = 2 into the expression:

2(2)cos(a) + 5cos(a) / (3cos(a) - sin(a))

Simplifying further:

4cos(a) + 5cos(a) / (3cos(a) - sin(a))

Combining the terms with a common denominator:

(4cos(a)(3cos(a) - sin(a)) + 5cos(a)) / (3cos(a) - sin(a))

Expanding the numerator:

(12cos²(a) - 4cos(a)sin(a) + 5cos(a)) / (3cos(a) - sin(a))

This is the simplified expression for 2sin(a) + 5cos(a) / 3cos(a) - sin(a) when tan(a) = 2.