What is the value of csc(arctan(15/8)) ?

The value of csc(arctan(15/8)) is 17/15

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csc(arctan(15/8))

csc (arctan (\frac{15}{8}))

\frac{17}{15}

Decimal

1.13333 \dots

Solution steps

csc (arctan (\frac{15}{8}))

Rewrite using trig identities:

csc (arctan (\frac{15}{8})) = \frac{1 + ( \frac{15}{8} ) ^{2}}{( \frac{15}{8} )}

Use the following identity:

csc (arctan (x)) = \frac{1 + x ^{2}}{x}

= \frac{1 + ( \frac{15}{8} ) ^{2}}{( \frac{15}{8} )}

= \frac{1 + ( \frac{15}{8} ) ^{2}}{\frac{15}{8}}

Simplify

= \frac{17}{15}

What is the value of csc(arctan(15/8)) ?
The value of csc(arctan(15/8)) is 17/15