Question

Soil equation for x sin inverse x + sin inverse 1 - x is equal cos inverse x

Answer 1

Answer:

Step-by-step explanation:asin(1-x) - 2 asin(x) = π/2  

sin(asin(1-x) - 2 asin(x)) = 1 .................. note: sin(π/2) = 1  

....... sin(ά - β) = sin(ά) cos(β) - cos(ά) sin(β)  

sin(asin(1-x)) cos(2asin(x)) - cos(asin(1-x))sin(2 asin(x)) = 1  

....... sin(asin(1-x)) = (1-x), cos(2asin(x)) = (1 - 2x²)  

....... cos(asin(1-x)) = √(2x - x²), sin(2 asin(x)) = 2x√(1 - x²)  

(1-x)(1 - 2x²) - 2x√(2x - x²) √(1 - x²) = 1  

....... has only one solution at x = 0 ....... graph it to see that  

If you plug-in x = 1/2, you get asin(1/2) - 2asin(1/2) = π/6 - 2π/6 = -π/6  

that's not π/2  

Answer: x = 0

Answer 2

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