What is the value of sin(2arcsin(1)) ?

The value of sin(2arcsin(1)) is 0

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sin(2arcsin(1))

sin (2 arcsin (1))

0

Solution steps

sin (2 arcsin (1))

Rewrite using trig identities:

2 sin (arcsin (1)) cos (arcsin (1))

sin (2 arcsin (1))

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (arcsin (1)) cos (arcsin (1))

= 2 sin (arcsin (1)) cos (arcsin (1))

Rewrite using trig identities:

sin (arcsin (1)) = 1

Use the following identity:

sin (arcsin (x)) = x

= 1

Rewrite using trig identities:

cos (arcsin (1)) = 0

cos (arcsin (1))

Rewrite using trig identities:

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

Use the following identity:

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

= 1 - 1^{2}

= 1 - 1^{2}

Simplify

= 0

= 2 \cdot 1 \cdot 0

Simplify

= 0

sec (\frac{17 π}{4})

cos (arctan (\frac{5}{12}))

cos (7 5^{\circ}) cos (1 5^{\circ})

tan (4 5^{\circ} - 3 0^{\circ})

sec (1 1^{\circ})