Is sin(40)=2*sin(20)*cos(20) ?

The answer to whether sin(40)=2*sin(20)*cos(20) is True

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prove sin(40)=2sin(20)cos(20)

prove

sin (4 0^{\circ}) = 2 \cdot sin (2 0^{\circ}) \cdot cos (2 0^{\circ})

True

Solution steps

sin (4 0^{\circ}) = 2 sin (2 0^{\circ}) cos (2 0^{\circ})

Manipulating left side

sin (4 0^{\circ})

Rewrite using trig identities

sin (4 0^{\circ})

= sin (2 \cdot 2 0^{\circ})

Use the Double Angle identity:

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

= 2 sin (2 0^{\circ}) cos (2 0^{\circ})

= 2 sin (2 0^{\circ}) cos (2 0^{\circ})

We showed that the two sides could take the same form

\Rightarrow True

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Is sin(40)=2*sin(20)*cos(20) ?
The answer to whether sin(40)=2*sin(20)*cos(20) is True