If angle a is 45 degrees and angle b is 60 degrees.
find sin(a)cos(b)
½ (sin(105) + sin(345))
½ (sin(105) - sin(345))
½ (sin(345) + cos(105))
½ (sin(345) - cos(105))

  (1/2)(sin(105°) +sin(345°))

Step-by-step explanation:

The relevant identity is ...

  sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))

This falls out directly from the sum and difference formulas for sine.

Here, you have α = 45° and β = 60°, so the relevant expression is ...

  sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))

Recognizing that -15° has the same trig function values that 345° has, this can be written ...

  sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

step-by-step explanation:

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