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

The value of 1/2 (arcsin(1)+1/2 sin(2arcsin(1))) is (arcsin(1))/2

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1/2 (arcsin(1)+1/2 sin(2arcsin(1)))

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

\frac{arcsin ( 1 )}{2}

Solution steps

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1))) = \frac{2 arcsin ( 1 ) + sin ( 2 arcsin ( 1 ) )}{4}

= \frac{2 arcsin ( 1 ) + sin ( 2 arcsin ( 1 ) )}{4}

Rewrite using trig identities:

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

= \frac{2 arcsin ( 1 ) + 2 sin ( arcsin ( 1 ) ) cos ( arcsin ( 1 ) )}{4}

Rewrite using trig identities:

sin (arcsin (1)) = 1

Rewrite using trig identities:

cos (arcsin (1)) = 0

= \frac{2 arcsin ( 1 ) + 2 \cdot 1 \cdot 0}{4}

Simplify

\frac{2 arcsin ( 1 ) + 2 \cdot 1 \cdot 0}{4} : \frac{arcsin ( 1 )}{2}

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

(3 sin (1 0^{\circ}) + cos (1 0^{\circ})) csc (4 0^{\circ})

\frac{tan ( 0 ) \cdot cos ( 0 )}{sin ( 0 )}

15 sin (8 5^{\circ})

sec (22 0^{\circ})

sin (π \frac{1}{4})

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