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

The value of sec^2(arctan(2))+csc^2(arccot(3)) is 15

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

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

15

Solution steps

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

Rewrite using trig identities:

sec (arctan (2)) = 5

sec (arctan (2))

Rewrite using trig identities:

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

Use the following identity:

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

= 1 + 2^{2}

= 1 + 2^{2}

Simplify

= 5

Rewrite using trig identities:

csc (arccot (3)) = 10

csc (arccot (3))

Rewrite using trig identities:

csc (arccot (3)) = \frac{1 + 3 ^{2}}{1 + 3 ^{2}}

Use the following identity:

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

= \frac{1 + 3 ^{2}}{1 + 3 ^{2}}

= \frac{1 + 3 ^{2}}{1 + 3 ^{2}}

Simplify

= 10

= (5)^{2} + (10)^{2}

Simplify

(5)^{2} + (10)^{2} : 15

(5)^{2} + (10)^{2}

(5)^{2} = 5

(5)^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

= 5^{\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

= 5

(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

= 5 + 10

Add the numbers:

5 + 10 = 15

= 15

= 15

arccos (0.375)

arccos (1.6)

32 sin (3 0^{\circ})

cos (4 5^{\circ}) sin (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

cos^{2} (4 π)

What is the value of sec^2(arctan(2))+csc^2(arccot(3)) ?
The value of sec^2(arctan(2))+csc^2(arccot(3)) is 15