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

The value of tan(arcsin((sqrt(3))/2)) is square root of 3

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tan(arcsin((sqrt(3))/2))

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

3

Decimal Notation

1.73205 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 3

tan (5 8^{\circ})

tan (6 5^{\circ})

tan (- 15 0^{\circ})

tan (4 3^{\circ})

arctan (\frac{π}{3})

What is the value of tan(arcsin((sqrt(3))/2)) ?
The value of tan(arcsin((sqrt(3))/2)) is square root of 3