Question

2sinx-cosx/2cosx+sinx=3; tg X?

Answer 1

2 sinx - cosx ÷ 2 cosx + sinx = 3
2 sins - cosx = 6 cosx + 3 sinx
- sinx = 7 cosx |: cosx
- tgx = 7
tgx = -7

Answer 2

To find the value of tangent (tan) of x when:

(2sinx - cosx) / (2cosx + sinx) = 3

You can start by multiplying both sides of the equation by the denominator (2cosx + sinx) to get rid of the fraction:

2sinx - cosx = 3(2cosx + sinx)

Now, let's expand and simplify the equation:

2sinx - cosx = 6cosx + 3sinx

Now, let's group like terms:

2sinx - 3sinx = 6cosx + cosx

• sinx = 7cosx

Now, divide both sides by cosx to isolate the tangent term (tanx):

• sinx/cosx = 7

Recall that the tangent of an angle x is defined as tanx = sinx/cosx. So, we have:

tanx = -7

So, the value of tangent (tan) of x is -7.