What is the value of sin(pi/6)cos(pi/3)+cos(pi/6)sin(pi/3) ?

The value of sin(pi/6)cos(pi/3)+cos(pi/6)sin(pi/3) is 1

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sin(pi/6)cos(pi/3)+cos(pi/6)sin(pi/3)

sin (\frac{π}{6}) cos (\frac{π}{3}) + cos (\frac{π}{6}) sin (\frac{π}{3})

1

Solution steps

sin (\frac{π}{6}) cos (\frac{π}{3}) + cos (\frac{π}{6}) sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= \frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2}

Simplify

\frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2} : 1

= 1

arctan (\frac{13}{4})

sin (\frac{9 π}{10})

150 cos (1 5^{\circ})

arctan (\frac{6}{2})

tan (arcsin (\frac{7}{9}))

What is the value of sin(pi/6)cos(pi/3)+cos(pi/6)sin(pi/3) ?
The value of sin(pi/6)cos(pi/3)+cos(pi/6)sin(pi/3) is 1