What is sin(a/2+a/2) ?

The solution to sin(a/2+a/2) is sin(a)

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simplify sin(a/2+a/2)

simplify

sin (\frac{a}{2} + \frac{a}{2})

sin (a)

Solution steps

sin (\frac{a}{2} + \frac{a}{2})

Rewrite using trig identities

= 2 sin (\frac{a}{2}) cos (\frac{a}{2})

Use the Double Angle identity:

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

= sin (2 \cdot \frac{a}{2})

Multiply

2 \cdot \frac{a}{2} : a

= sin (a)

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