What is the value of arcsin(cos(arcsin((sqrt(3))/2))) ?

The value of arcsin(cos(arcsin((sqrt(3))/2))) is pi/6

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arcsin(cos(arcsin((sqrt(3))/2)))

arcsin (cos (arcsin (\frac{3}{2})))

\frac{π}{6}

Solution steps

arcsin (cos (arcsin (\frac{3}{2})))

Rewrite using trig identities:

cos (arcsin (\frac{3}{2})) = 1 - (\frac{3}{2})^{2}

= arcsin 1 - (\frac{3}{2})^{2}

Simplify

= arcsin (\frac{1}{2})

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{6}

= \frac{π}{6}

tan (\frac{π}{7}) \cdot tan (\frac{2 π}{7}) \cdot tan (\frac{3 π}{7})

cos (\frac{π}{12}) + sin (\frac{π}{12})

tan (- 6)

\frac{5}{4} \cdot cos (3 0^{\circ})

cos^{2} (5 6^{\circ})

What is the value of arcsin(cos(arcsin((sqrt(3))/2))) ?
The value of arcsin(cos(arcsin((sqrt(3))/2))) is pi/6