Question

Sinbcos3b+cosbsin3b/sin2a

Answer 1

Никогда не любила тригонометрию((

Answer 2

To simplify the given expression, we can use trigonometric identities. The trigonometric identities we'll use are:

1. sin(3θ) = 3sin(θ) - 4sin^3(θ)
2. cos(3θ) = 4cos^3(θ) - 3cos(θ)

Let's simplify the expression step by step:

Expression: (sin(b)cos(3b) + cos(b)sin(3b)) / sin^2(a)

Step 1: Expand sin(3b) and cos(3b) using the identities mentioned above. sin(3b) = 3sin(b) - 4sin^3(b) cos(3b) = 4cos^3(b) - 3cos(b)

Step 2: Substitute the expanded values back into the expression. (sin(b)(4cos^3(b) - 3cos(b)) + cos(b)(3sin(b) - 4sin^3(b))) / sin^2(a)

Step 3: Distribute the terms. 4sin(b)cos^3(b) - 3sin(b)cos(b) + 3cos(b)sin(b) - 4cos(b)sin^3(b)

Step 4: Simplify the expression. 4sin(b)cos^3(b) - 3sin(b)cos(b) + 3sin(b)cos(b) - 4cos(b)sin^3(b)

The terms "-3sin(b)cos(b) + 3sin(b)cos(b)" cancel each other out.

Simplified expression: 4sin(b)cos^3(b) - 4cos(b)sin^3(b)

Finally, the expression is: 4sin(b)cos^3(b) - 4cos(b)sin^3(b) / sin^2(a)