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9514 1404 393
Answer:
(√17 -4√595)/102
Step-by-step explanation:
To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.
sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle
cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6
sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle
cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17
The sum of angles formula is ...
sin(α+β) = sin(α)cos(β) +cos(α)sin(β)
So, our sine is ...