Simplify tan(arcsin(( square root of 2)/2))

Problem

tan(arcsin(√(,2)/2))

Solution

1. Evaluate the inner inverse trigonometric function arcsin(√(,2)/2) by finding the angle θ in the interval [−π/2,π/2] such that sin(θ)=√(,2)/2

θ=π/4

2. Substitute the value of the angle back into the original expression.

tan(π/4)

3. Calculate the tangent of the angle using the unit circle or trigonometric identities.

tan(π/4)=1

Final Answer

tan(arcsin(√(,2)/2))=1

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