What is the value of tan^2(60)sec(30)sin(45) ?

The value of tan^2(60)sec(30)sin(45) is square root of 6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan^2(60)sec(30)sin(45)

Solution

tan^{2} (6 0^{\circ}) sec (3 0^{\circ}) sin (4 5^{\circ})

Solution

6

Decimal Notation

2.44948 \dots

Solution steps

tan^{2} (6 0^{\circ}) sec (3 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

Use the following trivial identity:

sec (3 0^{\circ}) = \frac{2 3}{3}

sec (3 0^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= (3)^{2} \frac{2 3}{3} \cdot \frac{2}{2}

Simplify

(3)^{2} \frac{2 3}{3} \cdot \frac{2}{2} : 6

(3)^{2} \frac{2 3}{3} \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 3 2 ( 3 ) ^{2}}{3 \cdot 2}

Cancel the common factor:

2

= \frac{3 2 ( 3 ) ^{2}}{3}

Cancel

\frac{3 2 ( 3 ) ^{2}}{3} : \frac{2 ( 3 ) ^{2}}{3}

\frac{3 2 ( 3 ) ^{2}}{3}

Apply radical rule:

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

= \frac{3 ^{\frac{1}{2}} 2 ( 3 ) ^{2}}{3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2 ( 3 ) ^{2}}{3 ^{\frac{1}{2}}}

Apply radical rule:

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

= \frac{2 ( 3 ) ^{2}}{3}

= \frac{2 ( 3 ) ^{2}}{3}

Simplify

(3)^{2} : 3

(3)^{2}

Apply radical rule:

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

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

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

= 3^{\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

= 3

= \frac{3 2}{3}

Cancel

\frac{2 \cdot 3}{3} : 23

\frac{2 \cdot 3}{3}

Apply radical rule:

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

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

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

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

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

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

Apply radical rule:

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

= 23

= 23

Apply radical rule:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= 6

Popular Examples

(14.088)/(tan(117.13))

\frac{14.088}{tan ( 117.1 3 ^{\circ} )}

csc(4/3)

csc (\frac{4}{3})

sin(75)+sin(120)-cos(150)+cos(165)

sin (7 5^{\circ}) + sin (12 0^{\circ}) - cos (15 0^{\circ}) + cos (16 5^{\circ})

4-4sin(pi/6)

4 - 4 sin (\frac{π}{6})

cos(pi/3)-2cos^2(pi/3)

cos (\frac{π}{3}) - 2 cos^{2} (\frac{π}{3})

Frequently Asked Questions (FAQ)

What is the value of tan^2(60)sec(30)sin(45) ?
The value of tan^2(60)sec(30)sin(45) is square root of 6