What is the value of 2sec^2(45)sec(30)-3cos(60)tan(60) ?

The value of 2sec^2(45)sec(30)-3cos(60)tan(60) is (7sqrt(3))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sec^2(45)sec(30)-3cos(60)tan(60)

Solution

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

Solution

\frac{7 3}{6}

Decimal Notation

2.02072 \dots

Solution steps

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

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 5^{\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}

= 2

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:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

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

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

Simplify

2 (2)^{2} \frac{2 3}{3} - 3 \cdot \frac{1}{2} 3 : \frac{7 3}{6}

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

2 (2)^{2} \frac{2 3}{3} = \frac{8 3}{3}

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

(2)^{2} = 2

(2)^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

= 2^{\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

= 2

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

Multiply fractions:

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

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

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= \frac{8 3}{3}

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3 3}{2}

= \frac{8 3}{3} - \frac{3 3}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Multiply each factor the greatest number of times it occurs in either

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

\frac{8 3}{3} :

multiply the denominator and numerator by

2

\frac{8 3}{3} = \frac{8 3 \cdot 2}{3 \cdot 2} = \frac{16 3}{6}

For

\frac{3 3}{2} :

multiply the denominator and numerator by

3

\frac{3 3}{2} = \frac{3 3 \cdot 3}{2 \cdot 3} = \frac{9 3}{6}

= \frac{16 3}{6} - \frac{9 3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{16 3 - 9 3}{6}

Add similar elements:

163 - 93 = 73

= \frac{7 3}{6}

= \frac{7 3}{6}

Popular Examples

1/(arctan(3/4))

\frac{1}{arctan ( \frac{3}{4} )}

sin^2(45)+8cos^2(30)

sin^{2} (4 5^{\circ}) + 8 cos^{2} (3 0^{\circ})

cos(0.6593)

cos (0.6593)

tan(30)tan(60)

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

sin(pi/4+pi/4)

sin (\frac{π}{4} + \frac{π}{4})

Frequently Asked Questions (FAQ)

What is the value of 2sec^2(45)sec(30)-3cos(60)tan(60) ?
The value of 2sec^2(45)sec(30)-3cos(60)tan(60) is (7sqrt(3))/6