What is the value of tan(arcsin(-1/2)+arccos(-(sqrt(3))/2)) ?

The value of tan(arcsin(-1/2)+arccos(-(sqrt(3))/2)) is -sqrt(3)

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tan(arcsin(-1/2)+arccos(-(sqrt(3))/2))

tan (arcsin (- \frac{1}{2}) + arccos (- \frac{3}{2}))

- 3

Solution steps

tan (arcsin (- \frac{1}{2}) + arccos (- \frac{3}{2}))

Use the following property:

arcsin (- x) = - arcsin (x)

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

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

Rewrite using trig identities:

\frac{tan ( arccos ( - \frac{3}{2} ) ) - tan ( arcsin ( \frac{1}{2} ) )}{1 + tan ( arccos ( - \frac{3}{2} ) ) tan ( arcsin ( \frac{1}{2} ) )}

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

Rewrite using trig identities:

tan (arccos (- \frac{3}{2})) = - \frac{3}{3}

Rewrite using trig identities:

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

= \frac{- \frac{3}{3} - \frac{3}{3}}{1 + ( - \frac{3}{3} ) \frac{3}{3}}

Simplify

\frac{- \frac{3}{3} - \frac{3}{3}}{1 + ( - \frac{3}{3} ) \frac{3}{3}} : - 3

= - 3

\frac{tan ( \frac{5 π}{8} ) - tan ( \frac{3 π}{8} )}{1 + tan ( \frac{5 π}{8} ) tan ( \frac{3 π}{8} )}

\frac{cot ^{2} ( - \frac{π}{4} )}{1 + 2 sin ( - \frac{π}{4} )}

tan (\frac{15 π}{6})

\frac{15.24}{tan ( 4 1 ^{\circ} )}

arctan (csc (\frac{π}{2}))

What is the value of tan(arcsin(-1/2)+arccos(-(sqrt(3))/2)) ?
The value of tan(arcsin(-1/2)+arccos(-(sqrt(3))/2)) is -sqrt(3)