What is the value of (sin(45)tan^2(60))/(cos(45)) ?

The value of (sin(45)tan^2(60))/(cos(45)) is 3

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(sin(45)tan^2(60))/(cos(45))

\frac{sin ( 4 5 ^{\circ} ) tan ^{2} ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

3

Solution steps

\frac{sin ( 4 5 ^{\circ} ) tan ^{2} ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

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}

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:

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

cos (4 5^{\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{2}{2}

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

Simplify

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

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

Apply the fraction rule:

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

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

(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 \cdot 2 \cdot \frac{2}{2}}{2}

Multiply the numbers:

3 \cdot 2 = 6

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

Multiply

6 \cdot \frac{2}{2} : 32

6 \cdot \frac{2}{2}

Multiply fractions:

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

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

Divide the numbers:

\frac{6}{2} = 3

= 32

= \frac{3 2}{2}

Cancel the common factor:

2

= 3

= 3

cos (π \frac{1}{6})

sec (arcsin (\frac{2}{5}))

4 cos^{2} (16 5^{\circ}) - 2

sin (3 0^{\circ}) + sin (12 0^{\circ}) + cos (24 0^{\circ}) - cos (33 0^{\circ})

arctan (sin (\frac{11 π}{4}))

What is the value of (sin(45)tan^2(60))/(cos(45)) ?
The value of (sin(45)tan^2(60))/(cos(45)) is 3