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

The value of cos(2arcsin((sqrt(2))/2)) is 0

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cos(2arcsin((sqrt(2))/2))

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

0

Solution steps

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

Rewrite using trig identities:

1 - 2 sin^{2} (arcsin (\frac{2}{2}))

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

Use the Double Angle identity:

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

= 1 - 2 sin^{2} (arcsin (\frac{2}{2}))

= 1 - 2 sin^{2} (arcsin (\frac{2}{2}))

Rewrite using trig identities:

sin (arcsin (\frac{2}{2})) = \frac{2}{2}

Use the following identity:

sin (arcsin (x)) = x

= \frac{2}{2}

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

Simplify

1 - 2 (\frac{2}{2})^{2} : 0

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

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

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

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

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

Apply exponent rule:

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

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

= \frac{2}{2 ^{2}}

Cancel the common factor:

2

= \frac{1}{2}

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= 1 - 1

Subtract the numbers:

1 - 1 = 0

= 0

= 0

arctan (\frac{8}{4.9})

cos (68 6^{\circ}) \cdot sec (3 4^{\circ}) + cos (1 8^{\circ}) \cdot sin (- 7 2^{\circ})

tan (- 72 0^{\circ})

arctan (10000)

4 sec^{2} (0) tan^{2} (0) + 2 sec^{4} (0)

What is the value of cos(2arcsin((sqrt(2))/2)) ?
The value of cos(2arcsin((sqrt(2))/2)) is 0