What is the value of tan(arcsin(7/8)) ?

The value of tan(arcsin(7/8)) is (7sqrt(15))/(15)

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tan(arcsin(7/8))

tan (arcsin (\frac{7}{8}))

\frac{7 15}{15}

Decimal Notation

1.80739 \dots

Solution steps

tan (arcsin (\frac{7}{8}))

Rewrite using trig identities:

tan (arcsin (\frac{7}{8})) = \frac{( \frac{7}{8} ) 1 - ( \frac{7}{8} ) ^{2}}{1 - ( \frac{7}{8} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{7}{8} ) 1 - ( \frac{7}{8} ) ^{2}}{1 - ( \frac{7}{8} ) ^{2}}

= \frac{\frac{7}{8} 1 - ( \frac{7}{8} ) ^{2}}{1 - ( \frac{7}{8} ) ^{2}}

Simplify

= \frac{7 15}{15}

cos (37. 5^{\circ}) cos (7.5)

\frac{tan ( 14 0 ^{\circ} ) - tan ( 6 0 ^{\circ} )}{1 + tan ( 14 0 ^{\circ} ) tan ( 6 0 ^{\circ} )}

(sec (\frac{π}{4}))^{2}

arcsin (- \frac{5}{13})

cot (- \frac{13 π}{6})

What is the value of tan(arcsin(7/8)) ?
The value of tan(arcsin(7/8)) is (7sqrt(15))/(15)