What is the value of tan(2arccos(1/4)) ?

The value of tan(2arccos(1/4)) is -(sqrt(15))/7

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tan(2arccos(1/4))

tan (2 arccos (\frac{1}{4}))

- \frac{15}{7}

Decimal Notation

- 0.55328 \dots

Solution steps

tan (2 arccos (\frac{1}{4}))

Rewrite using trig identities:

\frac{2 tan ( arccos ( \frac{1}{4} ) )}{1 - tan ^{2} ( arccos ( \frac{1}{4} ) )}

tan (2 arccos (\frac{1}{4}))

Use the Double Angle identity:

tan (2 x) = \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

= \frac{2 tan ( arccos ( \frac{1}{4} ) )}{1 - tan ^{2} ( arccos ( \frac{1}{4} ) )}

= \frac{2 tan ( arccos ( \frac{1}{4} ) )}{1 - tan ^{2} ( arccos ( \frac{1}{4} ) )}

Rewrite using trig identities:

tan (arccos (\frac{1}{4})) = 15

tan (arccos (\frac{1}{4}))

Rewrite using trig identities:

tan (arccos (\frac{1}{4})) = \frac{1 - ( \frac{1}{4} ) ^{2}}{( \frac{1}{4} )}

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{1}{4} ) ^{2}}{( \frac{1}{4} )}

= \frac{1 - ( \frac{1}{4} ) ^{2}}{\frac{1}{4}}

Simplify

= 15

= \frac{2 15}{1 - ( 15 ) ^{2}}

Simplify

\frac{2 15}{1 - ( 15 ) ^{2}} : - \frac{15}{7}

\frac{2 15}{1 - ( 15 ) ^{2}}

(15)^{2} = 15

(15)^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

= 1 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

= 15

= \frac{2 15}{1 - 15}

Subtract the numbers:

1 - 15 = - 14

= \frac{2 15}{- 14}

Apply the fraction rule:

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

= - \frac{2 15}{14}

Cancel the common factor:

2

= - \frac{15}{7}

= - \frac{15}{7}

\frac{sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}{tan ( 3 0 ^{\circ} )}

4 cos (3 0^{\circ}) + 6 sin (4 5^{\circ})

tan^{2} (\frac{5 π}{4})

5000 cos (3 0^{\circ})

sin (\frac{7}{12 \cdot π}) - cos (\frac{π}{12})

What is the value of tan(2arccos(1/4)) ?
The value of tan(2arccos(1/4)) is -(sqrt(15))/7