What is the value of tan(arcsin(3/5)+arccos(-1)) ?

The value of tan(arcsin(3/5)+arccos(-1)) is 3/4

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tan(arcsin(3/5)+arccos(-1))

tan (arcsin (\frac{3}{5}) + arccos (- 1))

\frac{3}{4}

Decimal Notation

0.75

Solution steps

tan (arcsin (\frac{3}{5}) + arccos (- 1))

Rewrite using trig identities:

\frac{tan ( arcsin ( \frac{3}{5} ) ) + tan ( arccos ( - 1 ) )}{1 - tan ( arcsin ( \frac{3}{5} ) ) tan ( arccos ( - 1 ) )}

tan (arcsin (\frac{3}{5}) + arccos (- 1))

Use the Angle Sum identity:

tan (s + t) = \frac{tan ( s ) + tan ( t )}{1 - tan ( s ) tan ( t )}

= \frac{tan ( arcsin ( \frac{3}{5} ) ) + tan ( arccos ( - 1 ) )}{1 - tan ( arcsin ( \frac{3}{5} ) ) tan ( arccos ( - 1 ) )}

= \frac{tan ( arcsin ( \frac{3}{5} ) ) + tan ( arccos ( - 1 ) )}{1 - tan ( arcsin ( \frac{3}{5} ) ) tan ( arccos ( - 1 ) )}

Rewrite using trig identities:

tan (arcsin (\frac{3}{5})) = \frac{3}{4}

tan (arcsin (\frac{3}{5}))

Rewrite using trig identities:

tan (arcsin (\frac{3}{5})) = \frac{( \frac{3}{5} ) 1 - ( \frac{3}{5} ) ^{2}}{1 - ( \frac{3}{5} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{3}{5} ) 1 - ( \frac{3}{5} ) ^{2}}{1 - ( \frac{3}{5} ) ^{2}}

= \frac{\frac{3}{5} 1 - ( \frac{3}{5} ) ^{2}}{1 - ( \frac{3}{5} ) ^{2}}

Simplify

= \frac{3}{4}

Rewrite using trig identities:

tan (arccos (- 1)) = 0

tan (arccos (- 1))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 0

= \frac{\frac{3}{4} + 0}{1 - \frac{3}{4} \cdot 0}

Simplify

= \frac{3}{4}

arccos (\frac{24}{25})

sin^{8} (\frac{π}{2})

sin (3 0^{\circ}) + sin (3 0^{\circ})

6 sin (8 0^{\circ})

sin (\frac{π}{15})

What is the value of tan(arcsin(3/5)+arccos(-1)) ?
The value of tan(arcsin(3/5)+arccos(-1)) is 3/4