What is the value of cos(2arcsin(8/17)) ?

The value of cos(2arcsin(8/17)) is 161/289

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cos(2arcsin(8/17))

cos (2 arcsin (\frac{8}{17}))

\frac{161}{289}

Decimal Notation

0.55709 \dots

Solution steps

cos (2 arcsin (\frac{8}{17}))

Rewrite using trig identities:

2 cos^{2} (arcsin (\frac{8}{17})) - 1

cos (2 arcsin (\frac{8}{17}))

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (arcsin (\frac{8}{17})) - 1

= 2 cos^{2} (arcsin (\frac{8}{17})) - 1

Rewrite using trig identities:

cos (arcsin (\frac{8}{17})) = \frac{15}{17}

cos (arcsin (\frac{8}{17}))

Rewrite using trig identities:

cos (arcsin (\frac{8}{17})) = 1 - (\frac{8}{17})^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{8}{17})^{2}

= 1 - (\frac{8}{17})^{2}

Simplify

= \frac{15}{17}

= 2 (\frac{15}{17})^{2} - 1

Simplify

2 (\frac{15}{17})^{2} - 1 : \frac{161}{289}

2 (\frac{15}{17})^{2} - 1

2 (\frac{15}{17})^{2} = \frac{450}{289}

2 (\frac{15}{17})^{2}

(\frac{15}{17})^{2} = \frac{1 5 ^{2}}{1 7 ^{2}}

(\frac{15}{17})^{2}

Apply exponent rule:

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

= \frac{1 5 ^{2}}{1 7 ^{2}}

= 2 \cdot \frac{1 5 ^{2}}{1 7 ^{2}}

Multiply fractions:

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

= \frac{1 5 ^{2} \cdot 2}{1 7 ^{2}}

1 5^{2} \cdot 2 = 450

1 5^{2} \cdot 2

1 5^{2} = 225

= 225 \cdot 2

Multiply the numbers:

225 \cdot 2 = 450

= 450

= \frac{450}{1 7 ^{2}}

1 7^{2} = 289

= \frac{450}{289}

= \frac{450}{289} - 1

Convert element to fraction:

1 = \frac{1 \cdot 289}{289}

= - \frac{1 \cdot 289}{289} + \frac{450}{289}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 289 + 450}{289}

- 1 \cdot 289 + 450 = 161

- 1 \cdot 289 + 450

Multiply the numbers:

1 \cdot 289 = 289

= - 289 + 450

Add/Subtract the numbers:

- 289 + 450 = 161

= 161

= \frac{161}{289}

= \frac{161}{289}

arccsc (\frac{1}{0})

15 \cdot sin (3 5^{\circ})

ln tan (\frac{π}{4}) + sec (\frac{π}{4})

6 \cdot sin (6 0^{\circ})

tan (arctan (- 2))

What is the value of cos(2arcsin(8/17)) ?
The value of cos(2arcsin(8/17)) is 161/289