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 Difference 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}

\frac{( tan ( 0 ) + 1 ) - ( tan ( - \frac{π}{6} ) + 1 )}{0 + \frac{π}{6}}

sin^{2} (15 0^{\circ})

arctan (tan (\frac{11 π}{9}))

- 2 sin (\frac{3 π}{2})

sin (5)

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