Question

3sin(П/2+а)/2cos (П–а), если а=7П/4

Answer 1

$\frac{3sin(\frac{\pi}{2}+a)}{2cos(\pi-a)}=\frac{3cos\ a}{-2cos\ a}=-\frac{3}{2}=-1,5$

Причем значение выражения постоянно и не зависит от величины угла а.

Ответ: -1,5.

Answer 2

We can start by plugging in the value of "a" into the given expression:

a = 7π/4

3sin(π/2 + a) / 2cos(π - a) = 3sin(π/2 + 7π/4) / 2cos(π - 7π/4)

We can simplify the trigonometric functions using the following identities:

sin(π/2 + θ) = cos(θ) cos(π - θ) = -cos(θ)

Using these identities, we get:

3sin(π/2 + 7π/4) / 2cos(π - 7π/4) = 3cos(7π/4) / (-2cos(π/4))

Next, we can simplify further using the trigonometric values for cosine and sine of 7π/4 and π/4 respectively:

cos(7π/4) = -√2/2 cos(π/4) = √2/2

Substituting these values, we get:

3cos(7π/4) / (-2cos(π/4)) = 3(-√2/2) / (-2√2/2) = 3(-√2/2) / (-√2) = 3/√2 = 3√2/2

Therefore, the value of the expression is 3√2/2.