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

The value of sec^2(arctan(2))-csc^2(arctan(3)) is 35/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec^2(arctan(2))-csc^2(arctan(3))

sec^{2} (arctan (2)) - csc^{2} (arctan (3))

\frac{35}{9}

Decimal Notation

3.88888 \dots

Solution steps

sec^{2} (arctan (2)) - csc^{2} (arctan (3))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= sec^{2} (arctan (2)) - \frac{10}{9}

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

= (5)^{2} - \frac{10}{9}

Simplify

(5)^{2} - \frac{10}{9} : \frac{35}{9}

(5)^{2} - \frac{10}{9}

(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

= 5 - \frac{10}{9}

Convert element to fraction:

5 = \frac{5 \cdot 9}{9}

= \frac{5 \cdot 9}{9} - \frac{10}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 9 - 10}{9}

5 \cdot 9 - 10 = 35

5 \cdot 9 - 10

Multiply the numbers:

5 \cdot 9 = 45

= 45 - 10

Subtract the numbers:

45 - 10 = 35

= 35

= \frac{35}{9}

= \frac{35}{9}

50 \cdot sin (4 0^{\circ})

6 cos (16 0^{\circ}) + 4 cos (29 0^{\circ})

sin (- 90 0^{\circ})

arcsin (\frac{11}{16})

arcsin (\frac{11}{15})

What is the value of sec^2(arctan(2))-csc^2(arctan(3)) ?
The value of sec^2(arctan(2))-csc^2(arctan(3)) is 35/9