What is the value of sec^2(arctan(3))+csc^2(arccot(4)) ?

The value of sec^2(arctan(3))+csc^2(arccot(4)) is 27

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sec^2(arctan(3))+csc^2(arccot(4))

sec^{2} (arctan (3)) + csc^{2} (arccot (4))

27

Solution steps

sec^{2} (arctan (3)) + csc^{2} (arccot (4))

Rewrite using trig identities:

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

Use the following identity:

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

= \frac{1 + 4 ^{2}}{1 + 4 ^{2}}

= sec^{2} (arctan (3)) + (\frac{1 + 4 ^{2}}{1 + 4 ^{2}})^{2}

Simplify

= sec^{2} (arctan (3)) + 17

Rewrite using trig identities:

sec (arctan (3)) = 10

sec (arctan (3))

Rewrite using trig identities:

sec (arctan (3)) = 1 + 3^{2}

Use the following identity:

sec (arctan (x)) = 1 + x^{2}

= 1 + 3^{2}

= 1 + 3^{2}

Simplify

= 10

= (10)^{2} + 17

Simplify

(10)^{2} + 17 : 27

(10)^{2} + 17

(10)^{2} = 10

(10)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (1 0^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 1 0^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 10

= 10 + 17

Add the numbers:

10 + 17 = 27

= 27

= 27

cot (arccos (\frac{- 2}{5}))

sec (2 \frac{π}{4})

arctan (\frac{- 4}{4 3})

16 \cdot sin (3 5^{\circ})

cos (42 0^{\circ}) \cdot tan (- 31 5^{\circ})

What is the value of sec^2(arctan(3))+csc^2(arccot(4)) ?
The value of sec^2(arctan(3))+csc^2(arccot(4)) is 27