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Omni-MATH / Evaluate sin (arcsin (0.4)+arcsin (0.5)) cdot sin (arcsin (0.5)-arcsin (0.4)) where for x∈[−1,1], arcsin (x) denotes the unique real number y∈[−π,π] such that sin(y)=x.

Problem

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problem

Evaluate $\sin (\arcsin (0.4)+\arcsin (0.5)) \cdot \sin (\arcsin (0.5)-\arcsin (0.4))$ where for x∈[−1,1]x \in[-1,1], $\arcsin (x)$ denotes the unique real number y∈[−π,π]y \in[-\pi, \pi] such that sin(y)=x\sin (y)=x.
Plain-text mathematical notation (without MathML)
Evaluate $\sin (\arcsin (0.4)+\arcsin (0.5)) \cdot \sin (\arcsin (0.5)-\arcsin (0.4))$ where for x∈[−1,1], $\arcsin (x)$ denotes the unique real number y∈[−π,π] such that sin(y)=x.
Original LaTeX notation
Evaluate $\sin (\arcsin (0.4)+\arcsin (0.5)) \cdot \sin (\arcsin (0.5)-\arcsin (0.4))$ where for $x \in[-1,1]$, $\arcsin (x)$ denotes the unique real number $y \in[-\pi, \pi]$ such that $\sin (y)=x$.

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Source and history

task_id
4dc5bd5b-74df-5b23-867b-d80fda56e9c8
task_key
test--4dc5bd5b-74df-5b23-867b-d80fda56e9c8
task_revision_id
1
config / split
/ test

Official source

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