What is the value of sec(arccot(4/7)) ?

The value of sec(arccot(4/7)) is (sqrt(65))/4

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sec(arccot(4/7))

sec (arccot (\frac{4}{7}))

\frac{65}{4}

Decimal Notation

2.01556 \dots

Solution steps

sec (arccot (\frac{4}{7}))

Rewrite using trig identities:

sec (arccot (\frac{4}{7})) = \frac{1 + ( \frac{4}{7} ) ^{2}}{( \frac{4}{7} )}

Use the following identity:

sec (arccot (x)) = \frac{1 + x ^{2}}{x}

= \frac{1 + ( \frac{4}{7} ) ^{2}}{( \frac{4}{7} )}

= \frac{1 + ( \frac{4}{7} ) ^{2}}{\frac{4}{7}}

Simplify

= \frac{65}{4}

\frac{7}{sin ( 2 5 ^{\circ} )}

csc (- \frac{11 π}{3})

2 cos (8)

sec (75 0^{\circ})

sin (- 54 0^{\circ})

What is the value of sec(arccot(4/7)) ?
The value of sec(arccot(4/7)) is (sqrt(65))/4