Question

Sin(П+В)сos(2П-В) ______________  tg(П-В)cos(П-В)

Answer 1

-sinB cosB           -sinB

--------------=  -------------- =-cosB

-tgB (-cosB)           tgB

Answer 2

To simplify the expression (sin(π+β)cos(2π-β)) / (tg(π-β)cos(π-β)), we can use trigonometric identities and properties:

1. sin(π+β) = -sin(β) (since sin(π) = 0)
2. cos(2π-β) = cos(-β) = cos(β) (since cos(2π) = 1 and cos(-θ) = cos(θ))
3. tan(π-β) = -tan(β) (since tan(π) = 0 and tan(-θ) = -tan(θ))
4. cos(π-β) = -cos(β) (since cos(π) = -1)

Now, we can simplify the expression step by step:

(sin(π+β)cos(2π-β)) / (tg(π-β)cos(π-β))

= (-sin(β)cos(β)) / (-tan(β)(-cos(β)))

= (sin(β)cos(β)) / (tan(β)cos(β))

Now, sin(β)cos(β) and tan(β)cos(β) have a common factor of cos(β). So, we can simplify further:

= (sin(β)cos(β)) / (tan(β)cos(β))

= sin(β) / tan(β)

Now, you can use the trigonometric identity:

tan(θ) = sin(θ) / cos(θ)

So, sin(β) / tan(β) can be simplified to:

= sin(β) / (sin(β) / cos(β))

= (sin(β) * cos(β)) / sin(β)

= cos(β)

Therefore, the simplified expression is just cos(β).