Question

2cos(п/2-a)*sin(п/2+a)*tg(п-a)​

Answer 1

Вот решение на фотографии

Answer 2

To simplify the expression 2cos(π/2-a) * sin(π/2+a) * tan(π-a), we'll use trigonometric identities to rewrite the trigonometric functions in a more manageable form. Recall the following trigonometric identities:

1. cos(π/2 - θ) = sin(θ)
2. sin(π/2 + θ) = cos(θ)
3. tan(π - θ) = -tan(θ)

Using these identities, we can simplify the given expression step by step:

Step 1: Replace cos(π/2 - a) with sin(a) using identity 1. 2 * sin(a) * sin(π/2 + a) * (-tan(a))

Step 2: Replace sin(π/2 + a) with cos(a) using identity 2. 2 * sin(a) * cos(a) * (-tan(a))

Step 3: Multiply sin(a) and cos(a). 2 * sin(a) * cos(a) * (-tan(a)) = -2 * sin(a) * cos(a) * tan(a)

Step 4: Use the identity tan(θ) = sin(θ) / cos(θ). -2 * sin(a) * cos(a) * tan(a) = -2 * sin(a) * cos(a) * (sin(a) / cos(a))

Step 5: Cancel out the common factor of cos(a). -2 * sin(a) * cos(a) * (sin(a) / cos(a)) = -2 * sin(a) * sin(a)

Step 6: Use the identity sin^2(θ) = (1 - cos(2θ))/2. -2 * sin(a) * sin(a) = -2 * (1 - cos(2a))/2

Step 7: Simplify further. -2 * (1 - cos(2a))/2 = -2 + 2cos(2a)

So, the simplified expression for 2cos(π/2-a) * sin(π/2+a) * tan(π-a) is -2 + 2cos(2a).